DOSEN PROFIL LENGKAP

referring to a multivector of a given degree p as a p-vector. Thus I've merged the articles under "Multivector", following Cartan: a multivector is an element...

the unit pseudoscalar (as would be suggested by the use of the term multivector), its complexification (the Dirac algebra) with i being the imaginary...

involving any kind of multivector (e.g. a 2-blade by a 3-blade, or a mixed-grade multivector by a 2-vector, or a mixed-grade multivector by another). Paolo...

the transformation rule for (n-1)-multivectors under general change of basis is different (he discusses multivectors starting p. 23). Weinreich calls pseudovectors...

think of M as a bilinear operator, and ψ as "half a vector" (or half a multivector) -- so it and its twin ψ~ are just the passive objects being operated...

another vector A Rotor (mathematics) or an improper rotation, a type of multivector in geometric algebra The second context (generic linear vector spaces...

(which I think most mathematicians would tend to call a k-vector or multivector, or just k-form in the more specific context of the exterior algebra...

the original language gave rise to some authors using this term for a multivector, in particular a 2-vector. A discussion of the English vs Continental...

an even multivector times an even multivector gives an even multivector, an even multivector times an odd multivector gives an odd multivector, and an...

in a Geometric Algebra style (meaning avoiding too much discussion of multivectors and exterior products). The idea is that once you "accept" that quaternions...

occurs in Multivector, which hapazardly switches between the terms without indicating their equivalence, or even defining a k-multivector. If its use...

) {\displaystyle {\mathcal {G}}(p,q)} , yields the GA definition, a multivector ψ {\displaystyle \psi } in G ( p , q ) {\displaystyle {\mathcal {G}}(p...

theory that the construction of dual quaternions yields a dual unit multivector that commutes with the quaternion unit multi vectors---they are constructed...

the subspace as you do for grassman algebras. This is also what is a multivector field . Therefore all this, although may be interesting, is not relevant...

direct/informative form. For example, the concept that generalises vectors is multivector, not bivector. A list of vague properties is given in the first paragraph...

different in 2004, qhen you wrote your comment). An outer product returns a matrix. An exterior product creates a multivector. Paolo.dL 13:07, 19 May 2007 (UTC)...

if you take the domain to be vector-valued and the coefficients to be multivector-valued ("Clifford numbers"). Ahlfors himself wrote a few papers about...

derivation I showed), but you still need a rule to know how to deal with multivectors of mixed grade and such. Teply (talk) 22:23, 26 May 2013 (UTC) Yes, once...

Euclidean vector. By the way, when editing the item p-vector, it appeared Multivector and Exterior algebra deserve to be merged. As I am not willing to do...

interpretation, complex numbers are being used because the geometric product and multivectors are an undertaught/underused mathematical formalism, despite being arguably...

grade (n-1) multivectors are called pseudovectors in geometric algebra. Consistent usage requires bivector = pseudovector in 3D. Can you comment directly...

extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra). In any case, the glossary at present has too...

And in reply to this last comment by Maschen: something that has bothered me for ages is that in application, most multivector objects in GA are restricted...

March 2018 (UTC) The § History says Cayley and Sylvester had a theory of multivectors. There is no reference to them. Does someone know a source for this assertion...

over the contributions for each pair of grades k and l of the general multivectors A and B, the contributions being as follows: for the contractive product...

multivectors in N-dimensional spaces, I moved the relevant discussion in Talk:Geometric algebra#Is there a convention about the order of multivector components...

submanifolds. In the (more natural) cooriented situation, you need to use multivector densities. But in any case, it's not our job on Wikipedia to present...

about this, both for quaternions per se and for more general kinds of multivectors. –jacobolus (t) 20:08, 17 June 2025 (UTC) Here's a source from the 1870s...

broader meaning than just rotation. One paper I'm reading says versors are multivectors that "have the property that they are a geometric product of vectors...

{\displaystyle \langle A\rangle _{k}} denotes the k-grade part of the multivector A. It's the only grade of the Clifford product which doesn't involve...

under transposition of the determinant), and has the nice property that multivectors made of orthonormal vectors are orthonormal. It is defined without respect...

linear algebra as a species of associative algebra with matrices as the multivectors, but am not confident that doing so is correct. Only today did I read...

through complex numbers as far as I know. Presumably your'e thinking of multivector-valued wavefunctions in geometric algebra which have the "spinorial"...

+I\mathbf {B} } and J = ρ − J {\displaystyle J=\rho -\mathbf {J} } are multivectors and I = γ 0 γ 1 γ 2 γ 3 {\displaystyle I=\gamma _{0}\gamma _{1}\gamma...

geometric algebra I think it would be better to instead add 'vectors' and 'multivectors' to Geometry § Objects. While we're at it, the current way both projective...

way Lounesto shows an analog from Dirac spinors to a set of real even multivectors (generalised rotors) in Cl1,3(R). However, note also p. 146, where Lounesto...

terminology to describe the various combinations is provided. For example, a multivector is a summation of k-fold wedge products of various k-values. A k-fold...

want an arbitrary different representation, it would be better to use multivectors (cf. Hestenes (2002) doi:10.1007/978-1-4612-0089-5_1) which is significantly...

a multiplicative inverse. One can use this to define, for example, a multivector differential calculus, which (I believe) can be quite usefully applied...

vector spaces (we do this all the time, whether in the form of tensors, multivectors or whatever). So let's not associate 3r + 3i 3D spacetime (with its six...

s}} and s is the smallest integer with that property. For your usual multivector, you of course get spin=1 except if x is entirely scalar+pseudoscalar...