Talk:Symmetric tensor

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. --Starwed 02:39, 16 November 2005 (UTC)

-- 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 symmetric tensor and a symmetric tensor of rank 2 (i.e., a symmetric matrix).
 * 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. VectorPosse 08:47, 28 September 2006 (UTC)

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.

need expert 02 nov 2006

errors in the article
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 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. --MarSch (talk) 11:06, 22 January 2008 (UTC)

Symmetric part of a tensor
The definition of the symmetric part of a tensor only makes sense in characteristic 0 (otherwise, we cannot divide by r!). —Preceding unsigned comment added by Mbroshi (talk • contribs) 21:32, 20 May 2011 (UTC)


 * In most cases, we are interested in vector spaces over either the reals or the complex numbers. So the characteristic (algebra) will be zero. If you know of a definition which works for other characteristics, please tell us. JRSpriggs (talk) 05:18, 21 May 2011 (UTC)
 * I see nothing wrong with pointing out that the characteristic needs to be zero in order to define the symmetric part. 166.137.141.96 (talk) 11:52, 21 May 2011 (UTC)

Symmetric vs. completely symmetric
Reading antisymmetric tensor, where there a clear distinction is made between antisymmetric on two indices and completely antisymmetric tensor, and this article where the term symmetric tensor is taken to mean completely symmetric tensor with no reference to symmetric on two indices, I get the feeling this article got it wrong in this respect. The concept symmetric on two (or any given subset of the) indices makes perfect sense and occurs frequently. — Quondum☏ 16:50, 3 May 2012 (UTC)


 * This is likely a math versus physics thing. For one, mathematicians would rarely talk about things being symmetric (or anti symmetric) on indices.  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).   Sławomir Biały  (talk) 17:24, 3 May 2012 (UTC)


 * 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 physicist's use of the term).  At least the symmetric tensor article is self-consistent in this sense (In mathematics...), whereas the antisymmetric tensor is not (In mathematics and theoretical physics...).   — Quondum☏ 18:32, 3 May 2012 (UTC)