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A basis: isn't the usual convention to take an ordered basis? Well, I think it is in the finite-dimensional case, anyway. This becomes awkward in other cases, though. Charles Matthews 16:49, 22 Apr 2005 (UTC)

I added a section in which I explaied that a standard basis is an ordered and orthonormal basis, but not necessarily vice versa. This can be deduced from the definition given in the introduction. So, it is a property, and I prefer to keep it separated from the definition (provided in the introduction). Paolo.dL (talk) 21:51, 22 March 2008 (UTC)Reply

The definition of a standard basis given here (see the lead) makes the assumption that a Euclidean space is defined by or has a unique Cartesian coordinate system. In general, a coordinate system for a Euclidean space is not unique any more than an orthogonal basis is unique. Hence, a standard basis (in the sense of this article) is only defined in terms of a specified Cartesian coordinate system, and does not exist for the general (coordinate-independent) Euclidean space. The article will have to be reworded with this in mind; I'm not sure whether I will do this. — Quondum^☏ 09:25, 7 April 2012 (UTC)Reply

Sentence needs rephrasing or clarification. It's very poor and hard to understand. To me at least. I had to read it five times although it's very simple. 1Minow (talk) 22:25, 25 March 2014 (UTC)Reply

Can you suggest something better? It is difficult to see how to improve it. —Quondum 04:09, 26 March 2014 (UTC)Reply

Well at least we could add an example matrix. I don't have much ideas. That's why I asked. ...Terribly sorry about the wrong edit. I didn't know. Thanks for correcting. 1Minow (talk) 18:03, 26 March 2014 (UTC)Reply

It was suggested back in November 2019 that Single-entry matrix should merge here. Perhaps, but does a Single-entry matrix have to be a Standard basis? For example, (0,1) is a single-entry matrix, but is (0,2)? If so, then perhaps sparse matrix is a better target. Klbrain (talk) 09:02, 19 July 2020 (UTC)Reply

Closing, given the absence of support for the proposal (over the course of a year). Klbrain (talk) 11:02, 14 September 2020 (UTC)Reply

In terms of 3D visualization, the vector diagram 3D_Vector.svg can be a little confusing at first (it was for me) regarding the fact that vector j appears to end at component vector a_z. Since this is actually a static 2D picture, it's all too easy for a puny human brain to misinterpret that and thus perceive those two vectors as intersecting, and a, a_z, and j as all lying in the y,z plane, rather than perceiving vector a as jutting out towards the viewer. If the standard basis vectors were shortened a bit (or a_y lengthened slightly) so that there was some space between a_z and the end of j, I think that would help vector a appear unambiguously 3D for most viewers, and thus make clearer what is going on in the diagram. — skoosh (háblame) 13:59, 12 July 2023 (UTC)Reply