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The article is suffering from some confusion between tensors and matrices. Currently the article says: "Symmetric rank 2 tensors can be diagonalized by choosing an orthogonal frame of eigenvectors." However that is nonsense as symmetric tensors map from one sort of vectors to their duals, so there is
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As far as it goes, that sounds fine. But since both the symmetric and antisymmetric concepts presumably occur with equal weight in both fields, this feels out of kilter: each article should then address use of the term in both fields (i.e. define the mathematician's use of the term, and also the
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This shouldn't be merged with symmetric matrix because a symmetric tensor of rank N, where N is not equal to 2, is a much different object than a symmetric matrix. I think there needs to be some clarification here, as the person who wrote it doesn't seem to understand the difference between a
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Whoever tagged this page probably should have added some notes in the talk page. ^_^ It's not clear why it needs cleaning up... while it provides almost no information, that's what the stub notice indicates. The only thing I see is that it perhaps implies that all tensors are second order.
327:. Rather this notion is expressed in terms of tensor products of appropriate spaces of tensors. So the bottom line for me is that this article uses the mathematicians' conventions (which is ok) and the other article uses the physicists' notation (also ok).
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no concept of eigenvectors, or the tensor is mixed covariant contravariant and it makes no sense to call it symmetric (except in a specific basis). If someone can clean these errors up that would be great, otherwise I will delete the erroneous passages. --
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the definition in the page is simply wrong. Symmetric tensor is not generalization of
Symmetric matrix, rather it is a tensor containing only itself as its isomera.
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I am removing the merge tag per the above comment and I agree that cleanup is necessary, although I do not have the time at the moment to do it.
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This is likely a math versus physics thing. For one, mathematicians would rarely talk about things being symmetric (or anti symmetric)
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The definition of the symmetric part of a tensor only makes sense in characteristic 0 (otherwise, we cannot divide by r!).
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I see nothing wrong with pointing out that the characteristic needs to be zero in order to define the symmetric part.
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In most cases, we are interested in vector spaces over either the reals or the complex numbers. So the
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Knowledge. If you would like to participate, please visit the project page, where you can join
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will be zero. If you know of a definition which works for other characteristics, please tell us.
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symmetric tensor and a symmetric tensor of rank 2 (i.e., a symmetric matrix).
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symmetric on two (or any given subset of the) indices
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