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210:. 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. —
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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
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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.
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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.
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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
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basis? Well, I think it is in the finite-dimensional case, anyway. This becomes awkward in other cases, though.
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appear unambiguously 3D for most viewers, and thus make clearer what is going on in the diagram. — skoosh
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Knowledge. If you would like to participate, please visit the project page, where you can join
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as jutting out towards the viewer. If the standard basis vectors were shortened a bit (or
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The definition of a standard basis given here (see the lead) makes the assumption that a
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Closing, given the absence of support for the proposal (over the course of a year).
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Can you suggest something better? It is difficult to see how to improve it. —
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th coordinate and 0's elsewhere". Last sentence in the first paragraph.
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