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mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial....

contains Linear A Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear A. Linear A is...

In linear algebra, a set of vectors is said to be linearly independent if there exists no vector in the set that is equal to a linear combination of the...

mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation...

For example, in geometry, two linearly independent vectors span a plane. To express that a vector space V is a linear span of a subset S, one commonly...

contains Linear B Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear B. Linear B is...

is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and...

three collinear, are linearly separable in two dimensions. The following example would need two straight lines and thus is not linearly separable: Notice...

different values of t1, t2, t3. In general, vectors v1, ... , vk are called linearly independent if t 1 v 1 + ⋯ + t k v k ≠ u 1 v 1 + ⋯ + u k v k {\displaystyle...

spanning set or generating set. If a spanning set S is linearly dependent (that is not linearly independent), then some element w of S is in the span of...

elements are linearly independent and every element of V is a linear combination of elements of B. In other words, a basis is a linearly independent spanning...

Linear referencing, also called linear reference system or linear referencing system (LRS), is a method of spatial referencing over linear or curvilinear...

space of A and so are linearly independent. This implies that c1 = c2 = ⋯ = cr = 0. It follows that Ax1, Ax2, ..., Axr are linearly independent. Every Axi...

polarization and plane of polarization for more information. The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric...

ratio of linear polynomials Linearly normal (AKA 1-normal), a property in algebraic geometry related to homogeneous coordinate rings Linearly unique polytope...

In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + … + a n x n + b = 0 , {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0...

{\displaystyle c_{i}\neq 0} are linearly dependent. Therefore, d {\displaystyle d} is at least the minimum number of linearly dependent columns. On another...

(ii) Any k-basis of A remains linearly independent over B. (iii) There exists a k-basis of A which remains linearly independent over B. (iv) If u i...

can be linearly extended from the linearly independent set of vectors S := { ( 1 , 0 ) , ( 0 , 1 ) } {\displaystyle S:=\{(1,0),(0,1)\}} to a linear map on...

In mathematics, linear interpolation (sometimes lerp) is a method of curve fitting using linear polynomials to construct new data points within the range...

then v1,...,vn are called linearly dependent; otherwise, they are linearly independent. Similarly, we can speak of linear dependence or independence...

Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities...

A linear alternator is an electromechanical type of alternator that is essentially a linear motor used as an electrical generator. An alternator generates...

quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form d r / d t...

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical...

Linear Technology Corporation was an American semiconductor company that designed, manufactured and marketed high performance analog integrated circuits...

analysis." The term "linear topology" goes back to Lefschetz's work. For each prime number p, Z {\displaystyle \mathbb {Z} } is linearly topologized by the...

the way that a linear polarizer would fully pass one angle of linearly polarized light unaltered, but would fully block any linearly polarized light...

Linear mode may refer to: Linear address mode Linear amplifier Linear mode (FET) Linear mode (JFET) Linear mode (MOSFET) Linear power supply Linear system...

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are...

operation is as a Lorentz-type actuator, in which the applied force is linearly proportional to the current and the magnetic field ( F → = I L → × B →...

In signal processing, linearizers are electronic circuits which improve the non-linear behaviour of amplifiers to increase efficiency and maximum output...

Linear mass density or simply linear density is defined in the International System of Quantities (ISQ) as the quotient of mass and length. It is also...

MaxLinear, Inc. is an American electronic hardware company. Founded in 2003, it provides highly integrated radio-frequency (RF) analog and mixed-signal...

into 'linear' and 'digital' lines. "Linear" here means "analog"; the linear line includes integrated circuits designed to process signals linearly, such...

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features...

linearly independent combinations (and therefore obtain innovative information) approaches 1. It should however be noted that, although random linear...

science, a linear grammar is a context-free grammar that has at most one nonterminal in the right-hand side of each of its productions. A linear language...

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In...

are linearly dependent, and the constant terms do not satisfy the dependence relation. A system of equations whose left-hand sides are linearly independent...

{\displaystyle P} is linearly unique (or linearly stable) if it has a unique origin symmetric realization up to linear transformations. The class of linear unique polytopes...

below.) If the functions are linearly dependent, then so are the columns of the Wrońskian (since differentiation is a linear operation), and the Wrońskian...

(the link function) to vary linearly with the predictors (rather than assuming that the response itself must vary linearly). For example, the case above...

combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference...

order may refer to: Linear order (linguistics), the order of words or phrases in linguistics Dense linear order, in mathematics Linearly ordered group This...

Linear city may refer to: Linear settlement Linear city (Soria design), an 1882 concept of city planning Linear city (Graves and Eisenman design), a 1965...

In the mathematical field of differential geometry, the term linear connection can refer to either of the following overlapping concepts: a connection...

are linearly independent if a linear combination results in the zero vector if and only if all its coefficients are zero. Linear subspace A linear subspace...

Non-linear media is a form of audiovisual media that can be interacted with by the viewer, such as by selecting television shows to watch through a video...

In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose...

A linear park is a type of park that is significantly longer than it is wide.[full citation needed] Linear parks are strips of public land running along...

patent granted in 1952. Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform. This is in contrast...

In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology...

is a linear classifier. It can only reach a stable state if all input vectors are classified correctly. In case the training set D is not linearly separable...

In mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant...

appear linearly. Linear regression may also refer to: The ordinary least squares method, one of the most popular methods for estimating a linear regression...

waveplates are the half-wave plate, which rotates the polarization direction of linearly polarized light, and the quarter-wave plate, which converts between different...

property of a material whose transmittance depends on the orientation of linearly polarized light incident upon it. As a technique, it is primarily used...

the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circular birefringence...

classify communication is to distinguish between linear transmission, interaction, and transaction models. Linear transmission models focus on how a sender transmits...

and horizontal linearly polarized light, or right- and left-handed circularly polarized light. Conversely, the two constituent linearly polarized states...

of linear equations, Li=ci for 1 ≤ i ≤ M, in variables X1, X2, ..., XN the equations are sometimes linearly dependent; in fact the number of linearly independent...

that (under this principle) every set can be linearly ordered. This assertion that every set can be linearly ordered is known as the ordering principle...

_{1},\lambda _{2}\in \mathbb {L} } are linearly independent over the rational numbers, then they are linearly independent over the algebraic numbers....

In computer science, linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list...

In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. A simpler definition...

combinations. affine combination A linear combination in which the sum of the coefficients is 1. basis In a vector space, a linearly independent set of vectors...

homogeneous linear differential equation of order n {\displaystyle n} there exists a fundamental system of n {\displaystyle n} linearly independent power...

In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle...

functions, any two nonzero meromorphic 1-forms yield linearly equivalent divisors. Any divisor in this linear equivalence class is called the canonical divisor...

program as a single contiguous address space." The CPU can directly (and linearly) address all of the available memory locations without having to resort...

‹ The template Infobox writing system is being considered for merging. › Linear Elamite was a writing system used in Elam during the Bronze Age between...

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the...

discontinuous linear maps are easy to construct in spaces that are not complete; on any Cauchy sequence e i {\displaystyle e_{i}} of linearly independent...

converge Q-linearly but will converge R-linearly with rate | r | m . {\textstyle {\sqrt[{m}]{|r|}}.} These examples demonstrate why the "R" in R-linear convergence...

superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the...

is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector...

(A-\lambda I)} are linearly dependent. Or the rank of the matrix is less than n. But as column rank = row rank, the rows are not linearly independent. Hence...

that it is also linearly independent to conclude that it is a basis. Suppose T ( S ) {\displaystyle T({\mathcal {S}})} is not linearly independent, and...

One common way is the number of linearly independent paths within it. A set S {\displaystyle S} of paths is linearly independent if the edge set of any...

any linear combination of functions equals the same linear combination of the derivatives of the functions; this property is known as linearity of differentiation...

In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency. The result is that...

a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, toset and loset are also used. The term chain is sometimes...

reflection. Rotators of linearly polarized light have found widespread applications in modern optics since laser beams tend to be linearly polarized and it is...

to combine known solutions into new solutions. In linear problems, for example, a family of linearly independent solutions can be used to construct general...

of 180 degrees, and can reach absolute extinction where T=0. For purely linearly polarized light, T has a sinusoidal dependence on angle θ with a period...

related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector...

linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data are linearly...

A linear actuator is an actuator that creates linear motion (i.e., in a straight line), in contrast to the circular motion of a conventional electric motor...

linear-frequency chirp or simply linear chirp, the instantaneous frequency f ( t ) {\displaystyle f(t)} varies exactly linearly with time: f ( t ) = c t + f...

Linear hashing (LH) is a dynamic data structure which implements a hash table and grows or shrinks one bucket at a time. It was invented by Witold Litwin...

Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital...

where "nonlinear model" is used to contrast with a linearly structured model, although the term "linear model" is not usually applied. One example of this...

In electronics, a linear regulator is a voltage regulator used to maintain a steady voltage. The resistance of the regulator varies in accordance with...

In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime...

A linear encoder is a sensor, transducer or readhead paired with a scale that encodes position. The sensor reads the scale in order to convert the encoded...

With this notation, one can write the elasticity matrix for any linearly elastic medium as: C i j k l ⇒ C α β = [ C 11 C 12 C 13 C 14 C 15 C 16...

with the standard inner product. The Gram–Schmidt process takes a finite, linearly independent set of vectors S = { v 1 , … , v k } {\displaystyle S=\{\mathbf...

caused by passing linearly polarized light through an optically active substance. Some chemical substances are optically active, and linearly polarized (uni-directional)...

Piecewise linear may refer to: Piecewise linear curve, a connected sequence of line segments Piecewise linear function, a function whose domain can be...

Linear control are control systems and control theory based on negative feedback for producing a control signal to maintain the controlled process variable...

v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across...

measurements. Integral linearity is a measure of the device's deviation from ideal linear behaviour. The most common denotation of integral linearity is independent...

{\displaystyle \lambda } . A chain is a linearly independent set of vectors. Definition: A set of n linearly independent generalized eigenvectors is a...

contraction. It can also be characterized as linear logic with weakening. The name "affine logic" is associated with linear logic, to which it differs by allowing...

injective and f ( A ) {\displaystyle f(A)} is linearly independent. A matroid with a representation is called a linear matroid, and if V {\displaystyle V} is...

bundles); see below. A complete linear system on X {\displaystyle X} is defined as the set of all effective divisors linearly equivalent to some given divisor...

The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be...

from the German Linearbandkeramik, it is also known as the Linear Band Ware, Linear Ware, Linear Ceramics or Incised Ware culture, falling within the Danubian I...

∂ f ( x ∗ ) {\displaystyle \partial f(x^{*})} is exactly balanced by a linear sum of forces ∂ h j ( x ∗ ) {\displaystyle \partial h_{j}(x^{*})} and ∂...

A linear response function describes the input-output relationship of a signal transducer, such as a radio turning electromagnetic waves into music or...

of labelled points is linearly separable. Conversely, with fixed dimensionality, for larger sample sizes the number of linearly separable sets of random...

torques on the disks (or drums) of the wheels. Rotational velocity decreases linearly to zero with constant angular deceleration. The frictional force, torque...

In convex optimization, a linear matrix inequality (LMI) is an expression of the form LMI ⁡ ( y ) := A 0 + y 1 A 1 + y 2 A 2 + ⋯ + y m A m ⪰ 0 {\displaystyle...

The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models...

Linear (pronounced: /lɪˈnɪər/; lin-EER) is an American freestyle-pop group from Fort Lauderdale, Florida. The lineup originally consisted of founder, lead...

volume the electric field in the crystal in front of the wave increases linearly, or the driver has to provide a constant current leakage. A Pockels cell...

Linear probing is a scheme in computer programming for resolving collisions in hash tables, data structures for maintaining a collection of key–value pairs...

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: <...

order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set S of more than...

diacritics can be characterized as less linear than those without. In the initial historical distinction, linear writing systems (e.g. the Phoenician alphabet)...

real numbers. An important application is to compute linear independence: a set of vectors are linearly independent if and only if the Gram determinant (the...

exponentials eα1, ..., eαn are linearly independent over the algebraic numbers. This equivalence transforms a linear relation over the algebraic numbers...

(1986-03-01). "A rapid Generalized Method of Bisection for solving Systems of Non-linear Equations". Numerische Mathematik. 49 (2): 123–138. doi:10.1007/BF01389620...

open intervals and rays. A topological space X is called orderable or linearly orderable if there exists a total order on its elements such that the order...

quarter-wave plate (QWP) and a linearly polarized filter (LPF). The QWP always transforms circularly polarized light into linearly polarized light. However...

of A, rank(A) = the maximum number of linearly independent rows or columns of A. If the matrix represents a linear transformation, the column space of the...

Linear medium may refer to: A material with linear elasticity An optical medium that obeys linear optics Nonlinear medium This disambiguation page lists...

triangle meshes by computing the lighting at the corners of each triangle and linearly interpolating the resulting colours for each pixel covered by the triangle...

to be linear if there exists a field K, an integer d and an injective homomorphism from G to the general linear group GLd (K) (a faithful linear representation...

data. It usually refers to the extent to which a pair of quantities are linearly related. More generally, an arbitrary relationship between variables is...

class, differing from each other by whether the carbon atoms are attached linearly or in a branched structure and whether the double bond has a cis or trans...

idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model. The resulting fitted model...

estimates the parameters of a logistic model (the coefficients in the linear or non linear combinations). In binary logistic regression there is a single binary...

has different colors when positioned at different angles with respect to linearly polarized light. The roots of the word are from Greek (from Ancient Greek...

similarly created from set relations. The set of all Dedekind cuts is itself a linearly ordered set (of sets). Moreover, the set of Dedekind cuts has the least-upper-bound...

linearly polarized sinusoidal one. "Plane" here means that the direction of propagation is unchanging and the same over the whole medium; "linearly polarized"...

organized in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks are trained using backpropagation and...

several definitions of R2 that are only sometimes equivalent. In simple linear regression (which includes an intercept), r2 is simply the square of the...

with "linear stage", though technically "linear slide" refers to a linear motion bearing, which is only a component of a linear stage. All linear stages...

Since reflections (and sky-light) tend to be at least partially linearly-polarized, a linear polarizer can be used to change the balance of the light in the...

absorption) of linearly polarized electromagnetic waves. Different levels of total transmission (reflection and absorption) for the same linearly polarized...

coefficients of the equation are real. These solutions can be shown to be linearly independent, by considering the Vandermonde determinant of the values of...

1-normal it is called linearly normal. A non-singular variety is projectively normal if and only if it is k-normal for all k ≥ 1. Linear normality may also...

linearization (or Carleman embedding) is a technique to transform a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear...

Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity...

(F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor...

second-order linear ordinary differential equations. It is employed when one solution y 1 ( x ) {\displaystyle y_{1}(x)} is known and a second linearly independent...

A linear castle is a castle that was designed to confront its attackers with a series of barriers/impediments in a line (hence the name). The principle...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns...

not linearly related to the other independent variables. Specifically, each independent variable can be decomposed into two parts: the part linearly related...

than one way; this means that the set of face cycles is linearly independent. As a linearly independent set of enough cycles, it necessarily forms a...

u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } are linearly dependent. Sedrakyan's inequality, also known as Bergström's inequality...

superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions...

cornering force increases approximately linearly for the first few degrees of slip angle, then increases non-linearly to a maximum before beginning to decrease...

rotational motion and linear motion: rotating the pinion causes the rack to be driven in a line. Conversely, moving the rack linearly will cause the pinion...

with respect to the other, is said to be non-Archimedean. For example, a linearly ordered group that is Archimedean is an Archimedean group. This can be...

current density vector, also a function of time and position. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity...

In computer science, a linear bounded automaton (abbreviated LBA) is a restricted form of Turing machine that functions as a more accurate model of a real-world...

Linear aeration is an aeration process that allows water to penetrate the soil and to be retained in the proper amounts. Additionally, it can also add...

minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function...

linear operator) To understand the utility of kernel PCA, particularly for clustering, observe that, while N points cannot, in general, be linearly separated...

Linear Recording is a recording studio complex located in Sydney, Australia, which was established by recording engineer Christopher Vallejo and Emren...

A linear settlement is a (normally small to medium-sized) settlement or group of buildings that are formed in a long line. Many of these settlements are...

simple description of all linearly ordered abelian groups. It is named after Hans Hahn. The theorem states that every linearly ordered abelian group G can...

In logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode...

A linear octree is an octree that is represented by a linear array instead of a tree data structure. To simplify implementation, a linear octree is usually...

lentiginous is used to describe other skin lesions that similarly proliferate linearly within the basal cell layer. Conditions characterized by lentigines include:...

eye than the original distance was. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer...

matrix is defective if and only if it does not have n {\displaystyle n} linearly independent eigenvectors. A complete basis is formed by augmenting the...

Linear heat detection (LHD) (also known as linear detection wire or linear heat detection cable or linear heat) is a very commonly used method of fire...

values of the individual random variables, and the expected value scales linearly with a multiplicative constant. Symbolically, for N {\displaystyle N} random...

dimension. The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with...

of the same finite dimension are linearly homeomorphic. Every separable infinite–dimensional Hilbert space is linearly isometrically isomorphic to the...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong...

linearly constrained Lagrangian method is used. This involves a sequence of major iterations, each of which solves (perhaps approximately) a linearly...

The linear range of a function is the portion of its overall range where the input is directly proportional to the output. The concept of a linear range...

SLAC National Accelerator Laboratory, originally named the Stanford Linear Accelerator Center, is a federally funded research and development center in...

(responsible, accountable, consulted and informed matrix; /ˈreɪsi/) or linear responsibility chart, is a project management technique that describes the...

permanent magnet lock the train into its lateral position. It can move linearly along the track but not off it. This is due to the Meissner effect and...

integer coefficients, for which only integer solutions are of interest. A linear Diophantine equation equates the sum of two or more unknowns, with coefficients...

ADALINE (Adaptive Linear Neuron or later Adaptive Linear Element) is an early single-layer artificial neural network and the name of the physical device...

single-mode optical fiber in which linearly polarized light, if properly launched into the fiber, maintains a linear polarization during propagation, exiting...

classification of division algebras. Specifically, the question is how many linearly independent smooth nowhere-zero vector fields can be constructed on a sphere...

inside a parallel plate capacitor depends linearly on the potential, the index of refraction depends linearly on the field (for crystals where Pockels...

where regressors are non-linearly dependent yet estimation may still be consistent, we might suspect the response depends linearly both on a value and its...

stating that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress). The wave equation...

A linear amplifier is an electronic circuit whose output is proportional to its input, but capable of delivering more power into a load. The term usually...

A partial linear space (also semilinear or near-linear space) is a basic incidence structure in the field of incidence geometry, that carries slightly...

MPC · JPL 187P/LINEAR P/1999 J5 P/2007 E3 LINEAR 9.53 0.1732 4.494 13.66 7.3 JFC – MPC · JPL 188P/LINEAR–Mueller P/1998 S1 P/2007 J7 LINEAR J. E. Mueller...

three are easily seen to be linearly independent, and therefore span all of R3. The last one then necessarily is a linear combination of the first three...

particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties...

and v(x) are two non-trivial continuous linearly independent solutions to a homogeneous second order linear differential equation with x0 and x1 being...

classified in the same manner as single equations, namely as a: System of linear equations, System of nonlinear equations, System of bilinear equations,...

margin. If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing the number...

be fixed-length or resizable. A linked list (also just called list) is a linear collection of data elements of any type, called nodes, where each node has...

Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters...

linear chromosome is a chromosome which is linear in shape, and contains terminal ends. In most eukaryotic cells, DNA is arranged in multiple linear chromosomes...

describe all the languages that linearly indexed grammars can describe. Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory...

numbers { z 1 , . . . , z n } {\displaystyle \{z_{1},...,z_{n}\}} that are linearly independent over Q {\displaystyle \mathbb {Q} } , the field extension Q...

\right)\mathbf {v} =0.} There will be 1 ≤ mi ≤ ni linearly independent solutions to each eigenvalue equation. The linear combinations of the mi solutions (except...

idiosyncratic modifications in the rules. Many of Fux's rules concerning the purely linear construction of melodies have their origin in solfeggio. Concerning the...

Linear drumming is a drum kit playing style in which no drum, cymbal, or other drum component hits simultaneously. Unlike other forms of time keeping and...

iterative method in machine learning for finding a linear decision boundary that separates two linearly separable classes. It was developed by Yu-Chi Ho...

polarized light can be converted into linearly polarized light by passing it through a quarter-waveplate. Passing linearly polarized light through a quarter-waveplate...

Linear (or Longitudinal) Timecode (LTC) is an encoding of SMPTE timecode data in an audio signal, as defined in SMPTE 12M specification. The audio signal...

challenges may be played in a different order. Conversely, a video game with linear gameplay will confront a player with a fixed sequence of challenges: every...

mathematics, the linear arboricity of an undirected graph is the smallest number of linear forests its edges can be partitioned into. Here, a linear forest is...

The decompression model is also referred to as the Linear–Exponential model or the Exponential–Linear model. The Mk15 rebreather supplies a constant partial...

vector representing the same state of polarization. In general, the wave is linearly polarized when the phase angles α x , α y {\displaystyle \alpha _{x},\alpha...

piecewise linear functions form monotone chains with respect to a horizontal line. Each segment of a polygonal chain is typically parametrized linearly, using...

In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

spacings and sizes of parallel lines. These barcodes, commonly referred to as linear or one-dimensional (1D), can be scanned by optical scanners known as barcode...

In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have...

Linear optics is a sub-field of optics, consisting of linear systems, and is the opposite of nonlinear optics. Linear optics includes most applications...

Comptes rendus hebdomadaires des séances de l'Académie des sciences. When a linearly polarized wave propagates perpendicularly to a magnetic field (e.g. in...

specifically, Linear A of Crete Linear B of Crete Linear Elamite This disambiguation page lists articles associated with the title Linear script. If an...

linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation. The non-linear Riccati...

abandoned him. The narration follows multiple perspectives and is told non-linearly, jumping between the contemporary 2011 and the past of both Samuel and...

A squall line, or quasi-linear convective system (QLCS), is a line of thunderstorms, often forming along or ahead of a cold front. In the early 20th century...

A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high...

In dosimetry, linear energy transfer (LET) is the amount of energy that an ionizing particle transfers to the material traversed per unit distance. It...

pixel computed to be at row 20.2, column 14.5 can be calculated by first linearly interpolating between the values at column 14 and 15 on each rows 20 and...

do not lie on a single linear space, and hence are linearly independent, and GL acts transitively on k-element sets of linearly independent vectors. PGL(2...

Although the absorption of waves does not usually depend on their intensity (linear absorption), in certain conditions (optics) the medium's transparency changes...

Greece, and China preferred the foot[citation needed]. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of 13.2 inches...

− 1 {\displaystyle \mathrm {Re} ^{-1}} , which means that the drag is linearly proportional to the speed, i.e. the drag force on a small sphere moving...

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization...

dynamics, an approximation whereby the Coriolis parameter, f, is set to vary linearly in space is called a beta plane approximation. On a rotating sphere such...

and Y {\displaystyle Y} are T {\displaystyle T} -linearly disjoint if and only if for all linearly independent sequences x 1 , … , x m {\displaystyle...

linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function...

Linear alkylbenzenes (sometimes also known as LABs) are a family of organic compounds with the formula C6H5CnH2n+1. Typically, n lies between 10 and 16...

the problem is in fact linear and the method finds the optimum in one iteration. If |λ| < 1, then the method converges linearly and the error decreases...

Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial...

module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, but, if the ring of the...

kernel of A are orthogonal to each of the row vectors of A. These two (linearly independent) row vectors span the row space of A—a plane orthogonal to...

and is an example of the more general V-model. Instead of moving down linearly, the process steps are bent upwards after the coding phase, to form the...

linearly independent, but the family contains the same element twice (since indexed differently) and is linearly dependent (same vectors are linearly...

potential between the working electrode and a reference electrode is swept linearly in time. Oxidation or reduction of species is registered as a peak or trough...

phenomenon may result from either a linear exposure or irritation. Conditions demonstrating linear lesions after a linear exposure to a causative agent include:...

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{...

Notation is a Braille code for encoding mathematical and scientific notation linearly using standard six-dot Braille cells for tactile reading by the visually...

manifold M {\displaystyle M\,} of dimension n is a set of n global smooth linearly independent vector fields. Given a manifold M {\displaystyle M\,} of dimension...

{\displaystyle A} ⁠ has linearly independent columns (then A + A = I {\displaystyle A^{+}A=I} ) and ⁠ B {\displaystyle B} ⁠ has linearly independent rows (then...

In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles...

in the study of dynamical systems, the Hartman–Grobman theorem or linearization theorem is a theorem about the local behaviour of dynamical systems...

i , . . . , X k i ) {\displaystyle (X_{1i},X_{2i},...,X_{ki})} must be linearly independent: one must not be able to reconstruct any of the independent...

In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements...

where the potential of the working electrode is ramped linearly versus time. Unlike in linear sweep voltammetry, after the set potential is reached in...

contaminated. There are four major types of skull fractures: linear, depressed, diastatic, and basilar. Linear fractures are the most common, and usually require...

of machine tool that uses linear relative motion between the workpiece and a single-point cutting tool to machine a linear toolpath. Its cut is analogous...

between the variable's values and the best predictions that can be computed linearly from the predictive variables. The coefficient of multiple correlation...

{dt}{p(t)y(t)^{2}}}} is a solution of the same equation and is linearly independent from y. Further, all solutions are linear combinations of these two solutions. In the...

a set of linearly independent paths of execution. The method normally uses McCabe cyclomatic complexity to determine the number of linearly independent...

one another and to the propagating direction, a transverse wave. While linearly polarized light occurs when the electric field vector oscillates only in...

Phase Linear was an audio equipment manufacturer founded by Bob Carver and Steve Johnston in 1970. While primarily known as a power amplifier company it...

A linear scale, also called a bar scale, scale bar, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart...

center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics...

The dual of a given linear program (LP) is another LP that is derived from the original (the primal) LP in the following schematic way: Each variable in...

Yamanashi test track (see below). The trainsets are popularly known in Japan as linear motor car (リニアモーターカー, rinia mōtā kā), though there are many technical variations...

leads to a contradiction. By Zorn's lemma, every linearly independent set is contained in a maximal linearly independent set K. This maximality implies that...

number density, two-dimensional areal number density, or one-dimensional linear number density. Population density is an example of areal number density...

almost immediately jump back to the very beginning of the story to proceed linearly from there. Usually the film will proceed past the supposed "ending" shown...

ISPRD of a bond is the difference between its yield to maturity and the linearly interpolated yield for the same maturity on an appropriate reference yield...

unqualified correlation coefficient, is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance...

limiting value ℓ {\textstyle \ell } is said to converge linearly, or more technically Q-linearly, if there is some number μ ∈ ( 0 , 1 ) {\textstyle \mu...

utilizes a non-linear structure, focusing on events throughout the life of the titular character rather than describing them in a linear narrative. From...

in two forms, open-chain (linear) or closed-chain (cyclic), that easily convert into each other in water solutions. The linear form of a pentose, which...

mathematician Niels Henrik Abel. Since Abel's identity relates to the different linearly independent solutions of the differential equation, it can be used to find...

V/m) is required. In this case, the polarization density P responds non-linearly to the electric field E of light. In order to obtain an electromagnetic...

O(n)} . Informally, this means that the running time increases at most linearly with the size of the input. More precisely, this means that there is a...

matrix A is singular exactly when its columns (and rows) are linearly dependent, so that the linear map x → A x {\displaystyle x\rightarrow Ax} is not one-to-one...

When any two sine waves of the same frequency (but arbitrary phase) are linearly combined, the result is another sine wave of the same frequency; this property...

{\displaystyle k} columns in A {\displaystyle A} which are linearly dependent. If all the columns are linearly independent, s p a r k ( A ) {\displaystyle \mathrm...

multiplied by itself, the result is itself All of its rows and columns are linearly independent. The principal square root of an identity matrix is itself...

In linguistics, word order (also known as linear order) is the order of the syntactic constituents of a language. Word order typology studies it from a...

A linear compressor is a gas compressor where the piston moves along a linear track to minimize friction and reduce energy loss during conversion of motion...

The E-plane and H-plane are reference planes for linearly polarized waveguides, antennas and other microwave devices. In waveguide systems, as in the electric...

whether to call leaves on the same tree "acuminate", "lanceolate", or "linear" could depend on individual judgement, or which part of the tree one collected...

whole. Categorization in this way yields two broad classes: linear and branching. In a linear hierarchy, the maximum degree is 1. In other words, all of...

also used by 16-bit OS/2 and Windows. This format is 16-bit. Linear Executable The Linear Executable (LE) format is mixed 16/32-bit and was introduced...

A first-order linear system of ODEs is a system in which every equation is first order and depends on the unknown functions linearly. Here, we consider...

matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points...

A linear combination of atomic orbitals (LCAO) is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum...

Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in...

Linear arithmetic synthesis, or LA synthesis, is a means of sound synthesis invented by the Roland Corporation when they released their D-50 synthesizer...

abelian groups. A subset {aα} of an abelian group A is linearly independent (over Z) if the only linear combination of these elements that is equal to zero...

important class of graded quadratic algebras is Koszul algebras. A quadratic-linear algebra is an algebra over a field with a presentation such that all relations...

approximate the kinematics of an object by assuming that the velocity changes linearly with time. Over short time intervals, we can often assume that the acceleration...

space spanned by the linearly independent vectors v1, ..., vr−1 and falls within the r-dimensional space spanned by the linearly independent vectors v1...

transverse U-cores. In this electric motor design, the force is produced by a linearly moving magnetic field acting on conductors in the field. Any conductor...

some square submatrix B {\displaystyle B} of A {\displaystyle A} with linearly independent columns such that B x 0 = b {\displaystyle B\mathbf {x} _{0}=\mathbf...

Euclidean space. For instance, linearly increasing the radius of a circle in Euclidean space increases its circumference linearly, while the same circle in...

A compact linear Fresnel reflector (CLFR) – also referred to as a concentrating linear Fresnel reflector – is a specific type of linear Fresnel reflector...

Linear Executable (LE) is file format for executable code designed for 32-bit protected mode operating systems. Originally used by the OS/2 operating system...

of coil current (I)—the field (H) is linearly dependent on I, B is linearly dependent on H and force is linearly dependent on the product BI. This relationship...

{\displaystyle S} is a closed set. Affine combination Convex combination Linear combination Convex Analysis and Minimization Algorithms by Jean-Baptiste...

In geometry, spherical linear interpolation, commonly abbreviated slerp, is a function which interpolates between two points on a sphere, such that spherical...

In linear algebra and functional analysis, the transpose or algebraic adjoint of a linear map between two vector spaces, defined over the same field, is...

real numbers. The real line is a linear continuum under the standard < ordering. Specifically, the real line is linearly ordered by <, and this ordering...

A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear...

housing it rotates in. Another type is the linear slider potentiometer, which has a wiper which slides along a linear element instead of rotating. Contamination...

1914) was the inventor of a linear scoring system for cricket before 1893. Unlike conventional scoring systems, the linear system shows balls faced by...

and bioinformatics. Methods are commonly divided into linear and nonlinear approaches. Linear approaches can be further divided into feature selection...

An arithmetic progression, arithmetic sequence or linear sequence is a sequence of numbers such that the difference from any succeeding term to its preceding...

lines set in the years 1964 and 2013. The two story lines are told non-linearly and are interwoven with use of match cuts, reflecting the themes of love...

phenomena often behave linearly (or approximately so) in a given operating range [further explanation needed]. Modeling them as linear functions can significantly...

matrix-valued function Ψ ( t ) {\displaystyle \Psi (t)} whose columns are linearly independent solutions of the system. Then every solution to the system...

In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates)...

The Linear Men are a fictional superhero team in the DC Comics universe. They first appeared in Adventures of Superman #476 (March 1991). The Linear Men...

PDE is called linear if it is linear in the unknown and its derivatives. For example, for a function u of x and y, a second order linear PDE is of the...

series and culture. The channel broadcasts on cable and satellite networks, linear television as well as streaming platforms including YouTube Channel and...

following condition: if x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} are linearly dependent then f ( x 1 , … , x n ) = 0 {\displaystyle f(x_{1},\ldots ,x_{n})=0}...

robustly fitting a line to sample points in the plane (a form of simple linear regression) by choosing the median of the slopes of all lines through pairs...

examples) The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are the same...

The Decision Linear assumption (DLIN assumption) is a computational hardness assumption used in elliptic curve cryptography. In particular, the DLIN assumption...

used to construct the curve as much as it reflects the observed data. For linear-algebraic analysis of data, "fitting" usually means trying to find the curve...

can avoid extracting square roots. Applicable to: m-by-n matrix A with linearly independent columns Decomposition: A = Q R {\displaystyle A=QR} where Q...

polarization, by means of two total internal reflections. If the incident beam is linearly polarized at 45° to the plane of incidence and reflection, the emerging...

thermal expansion linear with temperature (i.e. a constant coefficient of thermal expansion), the value of absolute zero was linearly extrapolated as the...

In linear algebra, linear transformations can be represented by matrices. If T {\displaystyle T} is a linear transformation mapping R n {\displaystyle...

\left(\left.{\frac {df^{t}(x)}{dx}}\right|_{x_{0}}t\right)} consisting of the linearly-independent solutions of the first-order approximation of the system. The...

connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem states that a linear operator between two Banach...

A linear-motion bearing or linear slide is a bearing designed to provide free motion in one direction. There are many different types of linear motion...

regression model are linearly dependent. Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship. When...

immunology, a linear epitope (also sequential epitope) is an epitope—a binding site on an antigen—that is recognized by antibodies by its linear sequence of...

Linear dynamical systems are dynamical systems whose evolution functions are linear. While dynamical systems, in general, do not have closed-form solutions...

LAPACK++, the Linear Algebra PACKage in C++, is a computer software library of algorithms for numerical linear algebra that solves systems of linear equations...

by the polymerization of ethylene, the monomer. LLDPE is a substantially linear polymer (polyethylene), with significant numbers of short branches. PE's...

inverse construction starts with a linearly ordered set and coils it up into a cyclically ordered set. Given a linearly ordered set L and an order-preserving...

Ultra-linear electronic circuits are those used to couple a tetrode or pentode vacuum-tube (also called "electron-valve") to a load (e.g. to a loudspeaker)...

linear isometry also necessarily preserves angles, therefore a linear isometry transformation is a conformal linear transformation. Examples A linear...

165P/LINEAR is a periodic comet in the Solar System. 165P/LINEAR has a perihelion distance of 6.8 AU, and is a Chiron-type comet with TJupiter smaller...

Non-linear editing (NLE) is a form of offline editing for audio, video, and image editing. In offline editing, the original content is not modified in...

and Phoenicans keeping fewer... The two systems of writing, pictorial and linear, which Dr. Evans has found to have been used in Crete, long before the Phoenician...

rollers pressed together with the strip between them. The rollers move linearly within the channel as they counter-rotate. During the motion each contact...

pictures and first-run original television series. Starz operates six 24-hour, linear multiplex channels; a traditional subscription video on demand service;...

compounds are referred to respectively as linear and angular furanocoumarins, so called since they exhibit a linear or angular chemical structure. The compounds...

Linear Flash is a PC card flash memory format. Linear Flash requires no battery support, unlike somewhat faster SRAM, and features read/write speeds much...

that acts linearly on the vectors (that is, the vectors between points of the space). In symbols, f {\displaystyle f} determines a linear transformation...

Linear partial information (LPI) is a method of making decisions based on insufficient or fuzzy information. LPI was introduced in 1970 by Polish–Swiss...

database, also known as a rowstore, the elements of the table are stored linearly as I.e. each row of the table is located one after the other. In this orientation...

function B i ( x ) {\displaystyle \mathbf {Bi({\boldsymbol {x}})} } are linearly independent solutions to the differential equation d 2 y d x 2 − x y =...

2,800 years; previously, Greek was recorded in writing systems such as Linear B and the Cypriot syllabary. The Greek language holds a very important place...

code-excited linear prediction (ACELP) is a speech coding algorithm in which a limited set of pulses is distributed as excitation to a linear prediction...

variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...

Mentha, also known as mint (from Greek μίνθα míntha, Linear B mi-ta), is a genus of flowering plants in the mint family, Lamiaceae. It is estimated that...

E_{y}} and so on. For a linear medium, only the first term of this equation is significant and the polarization varies linearly with the electric field...

input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., O(n)). During each iteration, the first remaining element...

Alashiya (Akkadian: 𒀀𒆷𒅆𒅀 Alašiya [a-la-ši-ia]; Ugaritic: 𐎀𐎍𐎘𐎊 ẢLṮY; Linear B: 𐀀𐀨𐀯𐀍 Alasios [a-ra-si-jo]; Hieratic "'irs3"), also spelled Alasiya...

application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Qi...

harder materials. When testing metals, indentation hardness correlates linearly with tensile strength. The differential depth hardness measurement was...

voltages at the ports and the currents flowing through them are still linearly related by the impedance matrix. The reciprocal of impedance is admittance...

non-linear, on-demand access to television content, this approach to broadcasting has since been referred to using the retronym linear (such as linear television...

connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(V + E)). A directed graph is called strongly connected...

finite-dimensional space, it often happens that the sets to discriminate are not linearly separable in that space. For this reason, it was proposed that the original...

point change in magnitude if a point load is applied to a member, and a linearly varying shear magnitude as a result of a constant distributed load. Similarly...

is "fed back" as input to the process, closing the loop. In the case of linear feedback systems, a control loop including sensors, control algorithms,...

columns of a parity-check matrix H are linearly independent while there exist d columns of H that are linearly dependent. The parity check matrix for...

In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given...

to 1. Quadratic probing in which the interval between probes increases linearly (hence, the indices are described by a quadratic function). Double hashing...

as PAM or pAAM) is a polymer with the formula (-CH2CHCONH2-). It has a linear-chain structure. PAM is highly water-absorbent, forming a soft gel when...

of linear measurement until 1 January 2023. The Mendenhall Order of 1893 defined the yard as exactly 3600⁄3937 meters, with all other units of linear measurement...

rotary motion can be adapted to function as a linear actuator (which produces a linear motion, but is not a linear motor). Another broad classification of actuators...

Quotient space (topology), in case of topological spaces Quotient space (linear algebra), in case of vector spaces Quotient space of an algebraic stack...

bounding the norms of non-linear operators acting on Lp spaces. Marcinkiewicz' theorem is similar to the Riesz–Thorin theorem about linear operators, but also...

hold by the definition of linearity. However, even in a linear system in which the power quantity is the product of two linearly related quantities (e.g...

multiplexed channels in August 1991. The service currently operates six 24-hour, linear multiplex channels as well as a traditional subscription video on demand...

certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used...

with the alternative linear forms of the Michaelis–Menten equation such as the Hanes–Woolf plot or Eadie–Hofstee plot, all linearized forms of the Michaelis–Menten...

of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at...

also be 0. This leaves in the original linear combination just the pi terms, which are assumed to be linearly independent, and so their coefficients must...

linear or ordinary least squares and nonlinear least squares, depending on whether or not the model functions are linear in all unknowns. The linear least-squares...

itself evolves linearly. Then standard methods can be used to solve the linear difference equation in x t {\displaystyle x_{t}} . The linear recurrence of...

equality if and only if x {\displaystyle x} and y {\displaystyle y} are linearly dependent. Parallelogram law ‖ x + y ‖ 2 + ‖ x − y ‖ 2 = 2 ‖ x ‖ 2 + 2...

columns of the outer product are all proportional to u. Thus they are all linearly dependent on that one column, hence the matrix is of rank one. ("Matrix...

of all linearly independent subsets of V. Since V is not the zero vector space, there exists a nonzero element v of V, so P contains the linearly independent...

relates nonlinear products caused by the third-order nonlinear term to the linearly amplified signal, in contrast to the second-order intercept point that...

onto the state ϕ , {\displaystyle {\boldsymbol {\phi }},} to find how linearly dependent two states are, etc. For the vector space C n {\displaystyle...

space of sequences (a sequence space). Sequence transformations include linear mappings such as discrete convolution with another sequence and resummation...

computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, fast Fourier transform...

the series depends linearly on its own past values (lags), while the MA component specifies that the current value depends on a linear combination of past...

user-defined) rule for comparing elements. A data structure is said to be linear if its elements form a sequence. Array Associative array Bit array Bit field...

Windows systems for uncompressed audio. The usual bitstream encoding is the linear pulse-code modulation (LPCM) format. WAV is an application of the Resource...

times during its nominal 25-month mission; the crucial technology is a linear variable filter, as demonstrated by LEISA on New Horizons. It will classify...

spatial locality, occurs when data elements are arranged and accessed linearly, such as traversing the elements in a one-dimensional array. Locality is...

tracking, compositing, and animation. It also functions as a very basic non-linear editor, audio editor, and media transcoder. In 2019, the program won an...

is the maximum number of linearly independent row vectors of the matrix, which is the same as the maximum number of linearly independent column vectors...

that there is only one solution of this equation; if there were, say, two linearly independent ground states, we would get two independent chains of eigenvectors...

means a linear dimension (measured, for example, in millimeters or inches). For an optical instrument with an eyepiece as an example, the linear dimension...

the Cretan hieroglyphs and later in the Linear A syllabary. As the Cretan hieroglyphs are undeciphered and Linear A only partly deciphered, the Minoan language...

linear type, to the point that the terms are often used interchangeably, but there is in fact a distinction: actual linear typing allows a non-linear...

Gauss's laws. For linear algebraic equations, one can make 'nice' rules to rewrite the equations and unknowns. The equations can be linearly dependent. But...

nonlinear optimal control problem given in the previous section is the linear quadratic (LQ) optimal control problem. The LQ problem is stated as follows...

the concept of emergence, such as: linear behaviour emergence from non linear equations as in solitons or linear emergence from ensemble averages, emergence...

nucleotide sequences associated with specialized proteins at the ends of linear chromosomes (see Sequences). Telomeres are a widespread genetic feature...

depending on the monomers and reaction conditions: A polymer may consist of linear macromolecules containing each only one unbranched chain. In the case of...

which mainly differ by the degree of linearity vs branching. LDPE can be further classified: LDPE and linear low-density PE. The former is produced...

Photoshop uses. The result of applying several of these modes depends linearly on the pixel level of the top layer. In such cases, when the top layer...

to a known curve can be found by sampling the curve and interpolating linearly between the points. An algorithm for computing the most significant points...

theorem Measure of non-compactness Banach–Mazur theorem Bounded linear operator Continuous linear extension Compact operator Approximation property Invariant...

stories share a common setting or set of characters with the aim of telling a linear story from beginning to end, with the individual chapters, however, refracting...

valid derivation in linear logic). The first such criterion is the long-trip criterion, which was described by Jean-Yves Girard. Linear logic Ludics Geometry...

family was designed to smoothly interpolate between a linear function and the Rectified linear unit (ReLU) function. When considering positive values...

molecules with idealised C2h symmetry. Within this the Au(I) centers are linearly coordinated with a Cl-Au-Cl bond angle of 175.0° (close to the ideal value...

energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corresponding SI unit is the joule, equal...

Linear is a 2009 film directed by Anton Corbijn. The film includes music from U2's 2009 studio album, No Line on the Horizon, and was included on both...

Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied...

process, non-linear (analog) film editing, has mostly been replaced by digital or video editing software, which operates as a non-linear editing (NLE)...

The criterion for inclusion in this list is the ability to perform non-linear video editing. Most modern transcoding software supports transcoding a portion...

radiation detector in order to characterise the radiation beams from medical linear accelerators. Typically, an ionisation chamber and water phantom are used...

rises proportionate to the square of the number of people in it, but only linearly with their fighting ability. The first three of these conclusions are obvious...

Japanese manga and anime, and its action-based fighting system called the "Linear Motion Battle System". Multiple people have become linked with the series...

(Math 55b). Previously, the official title was Honors Advanced Calculus and Linear Algebra. The course has gained reputation for its difficulty and accelerated...

) = 0 {\displaystyle y(t+1)=0} otherwise. It can be used to represent linearly separable boolean functions (for example, AND, OR, NOR) but not, for example...

a system is always linearly independent. Despite the name, an orthonormal basis is not, in general, a basis in the sense of linear algebra (Hamel basis)...

velocity saturation dominates, the saturation drain current is more nearly linear than quadratic in VGS. At even shorter lengths, carriers transport with...

A railgun or rail gun, sometimes referred to as a rail cannon, is a linear motor device, typically designed as a ranged weapon, that uses electromagnetic...

science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex...

crystal without a magnetic field, spatial translations are represented linearly and the corresponding translation operators commute with one another and...

important information first. Linear note-taking is the process of recording information in the order in which you receive it. Linear notes are typically chronological...

because of Newton's third law: the weight that one would feel standing in a linearly accelerating spacecraft would not be a true gravitational pull, but simply...

Phacelia linearis, the linear-leaved phacelia or threadleaf phacelia, is a species of phacelia. Phacelia linearis is an annual herb producing a branching...

usually a liquid. In a Pockels cell, the change in birefringence varies linearly with the electric field, and the material is usually a crystal. Non-crystalline...

linear molecular geometry describes the geometry around a central atom bonded to two other atoms (or ligands) placed at a bond angle of 180°. Linear organic...

particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy...

{T} }X} Assuming the columns of X {\displaystyle X} are linearly independent so that X T X {\displaystyle X^{\operatorname {T} }X} is invertible...

point on the screw's rim moves a distance of 2πr, while its shaft moves linearly by the lead distance l. So the distance ratio is distance ratio ≡ d in...

minichromosome. Plasmids are generally circular, but examples of linear plasmids are also known. These linear plasmids require specialized mechanisms to replicate...

size of a linearly independent subset. In a vector space consisting of a single point (which must be the zero vector 0), there is no linearly independent...

In computer science, a linear graph grammar (also a connection graph reduction system or a port graph grammar) is a class of graph grammar on which nodes...

between two complex vector spaces is said to be antilinear or conjugate-linear if f ( x + y ) = f ( x ) + f ( y )  (additivity)  f ( s x ) = s ¯ f ( x...

infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by k arbitrary functions and their derivatives up to order m, then the...

convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response...

When they have opposite signs, ℓ ( y ) {\displaystyle \ell (y)} increases linearly with y, and similarly if | y | < 1 {\displaystyle |y|<1} , even if it has...

continuous linear operators from X {\displaystyle X} into Y {\displaystyle Y} . Suppose that F {\displaystyle F} is a collection of continuous linear operators...

Gröbner basis § Leading term, coefficient and monomial. In linear algebra, a system of linear equations is frequently represented by its coefficient matrix...

The next most simple spline has degree 1. It is also called a linear spline. A closed linear spline (i.e, the first knot and the last are the same) in the...

PDF417 is a stacked linear barcode format used in a variety of applications such as transport, identification cards, and inventory management. "PDF" stands...

field limit it is expected that a flux will be linearly proportional to an applied field. In the linear case the flux and the force are said to be conjugate...

blocking will only work if the attacking piece is a type that can move linearly an indefinite number of squares such as a queen, rook, or bishop and there...

In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way...

In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v1, v2, ..., vn such that...

context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative...

Linear video editing is a video editing post-production process of selecting, arranging, and modifying images and sound in a predetermined, ordered sequence...

… , A r − 1 b } {\displaystyle \{b,Ab,A^{2}b,\ldots ,A^{r-1}b\}} are linearly independent unless r > r 0 {\displaystyle r>r_{0}} , K r ( A , b ) ⊂ K...

This list of linear television channels in the United Kingdom refers to television in the United Kingdom which is available from digital terrestrial, satellite...

included on, a function generator which creates an electrical waveform with a linearly varying frequency and a constant amplitude. Sweep generators are commonly...

algorithms: linear, binary, and hashing. Linear search algorithms check every record for the one associated with a target key in a linear fashion. Binary...

Frakefamide (INN) is a synthetic, fluorinated linear tetrapeptide with the amino acid sequence Tyr-D-Ala-(p-F)Phe-Phe-NH2 which acts as a peripherally-specific...

), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b")...

with a large village green. The old railway line is now known as Culcheth Linear Park. The name Culcheth is first attested in 1201, in the form Culchet;...

approximately lie on the identity line y = x. If the distributions are linearly related, the points in the Q–Q plot will approximately lie on a line, but...

out of the hypergeometric series 2F1(a, b; c; z). The equation has two linearly independent solutions. At each of the three singular points 0, 1, ∞, there...

any partially ordered set. A linearly ordered set that is dense and has the least upper bound property is called a linear continuum. Let S be a non-empty...

reluctance linear motors (SRLMs) (also known as linear switched reluctance motors (LSRMs), variable reluctance linear motor or switched reluctance linear machines)...

projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional...

boundedness principle states that a pointwise bounded family of continuous linear operators between Banach spaces is equicontinuous. Let X and Y be two metric...

which has a full length linear stroke on its right, should not be confused with turned script a, ⟨ɒ⟩, which has the linear stroke on its left and corresponds...

interactive music video platform founded in the Netherlands. The service operates linear and interactive television networks, and on-demand streaming services. XITE-branded...

documentaries, and special behind-the-scenes features. It operates five 24-hour linear channels and offers a traditional subscription video-on-demand service called...

Comet 252P/LINEAR is a Jupiter-family comet and near-Earth object discovered by the Lincoln Near-Earth Asteroid Research (LINEAR) survey on 7 April 2000...

main types of broaching: linear and rotary. In linear broaching, which is the more common process, the broach is run linearly against a surface of the...

coding theory, the dual code of a linear code C ⊂ F q n {\displaystyle C\subset \mathbb {F} _{q}^{n}} is the linear code defined by C ⊥ = { x ∈ F q n...

this corresponds to a change in the mean anomaly, which indeed increases linearly with time. Orbital period ( P ) — the time it takes for the orbiting body...

surrounding The High Fort (Mooney's Fort/Lios Ard) in Fortlands and built out linearly on the main road from there. The town's name, in the Irish language, was...

The Linear Scaffold is the debut studio album by Norwegian avant-garde metal band Solefald. It was released in 1997, through Avantgarde Records. The cover...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

Analysis of covariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable...

numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural...

includes sorting, searching, data structures, computational geometry, and linear programming, VLSI, distributed computing, parallel processing, computer...

Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to...

preprocesses a tree in linear time to provide constant-time LCA queries. In general DAGs, similar algorithms exist, but with super-linear complexity. The lowest...

using grammatical and lexical knowledge for comprehension rather than linearly decoding texts. Top-down proteomics, a method for protein analysis Top-down...

may be specified by a linear inequality, derived from the linear equation that specifies the defining hyperplane. A strict linear inequality specifies...

quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum...

finite family ( fi )i∈I of distinct monoid homomorphisms  fi : M → k is linearly independent. In other words, every family (αi)i∈I of elements αi ∈ k satisfying...

type. Here we can store 6 elements they will be stored linearly but starting from first row linear then continuing with second row. The above array will...

typically have an input and an output, and the productivity is usually linear to running speed. There is no formal guideline for what should be called...

{\displaystyle n} columns are linearly independent, then each of the n {\displaystyle n} state variables is viewable through linear combinations of the output...

{\displaystyle V} and a basis E {\displaystyle E} on that space, one can define a linearly independent set in V ∗ {\displaystyle V^{*}} called the dual set. Each...

Rank (type theory) Rank of an abelian group, the cardinality of a maximal linearly independent subset Rank of an elliptic curve Rank of a free module Rank...

channels of both are linearly related to each other, both Cb and U are related linearly to (B-Y), and both Cr and V are related linearly to (R-Y). Chroma...

that manipulates polarized light. It separates light into two separate linearly polarized outgoing beams with orthogonal polarization. The two beams are...

Fred Meijer White Pine Trail State Park is a 92-mile (148 km) long linear state park in the U.S. state of Michigan. The trail extends from northern Grand...

{\displaystyle E} by taking the independent sets of M {\displaystyle M} to be the linearly independent subsets of E {\displaystyle E} . The validity of the independent...

500 earthquakes followed in the next 2 months. These events resulted in a linear cumulative seismicity rate with a b value of nearly 1.0, which is an unusual...

The Hubbert linearization is a way to plot production data to estimate two important parameters of a Hubbert curve, the approximated production rate of...

science). This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist...

a parametric space curve. In physical space, a 1D subspace is called a "linear dimension" (rectilinear or curvilinear), with units of length (e.g., metre)...

performing the post-production video editing of digital video sequences on a non-linear editing system (NLE). It has replaced traditional flatbed celluloid film...

increased or decreased by a fixed amount on every iteration of a loop or is a linear function of another induction variable. For example, in the following loop...

Any n-dimensional PL manifold that is collapsible is in fact piecewise-linearly isomorphic to an n-ball. Discrete Morse theory – Combinatorial approach...

additive identity. In linear algebra, a basis of a vector space V is a linearly independent subset B such that every element of V is a linear combination of...

kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. Hobson, E. W. (1933). "James Mercer...

beginning in August 2010. The epicenters of earthquakes in the swarm showed a linear distribution, with a clear overall shift in activity towards the southwest...

made up of different atlases, with different constraints, such as linearly/non-linearly aligned and symmetric or non-symmetric brain hemispheres. Most neuroimaging...

Cutting Stroke: The downward linear motion of the cutter spindle together with the cutter . Return Stroke: The upward linear travel of the spindle and cutter...

generators that were invented by George Marsaglia. They are a subset of linear-feedback shift registers (LFSRs) which allow a particularly efficient implementation...