Talk:Antisymmetric tensor

Removed proof
Removed proof because of notational problems and incompleteness. On a related note, is the dual of antisymmetric covariant tensor always an antisymmetric contravariant tensor? This may be relevant to the proof (actually, the statement its trying to prove) and may be an interesting fact to include in this page in its own right. Saligron 05:29, 30 January 2007 (UTC)

Merge into tensor?
The portion on symmetric and antisymmetric parts is not directly about antisymmetric tensors, and the remaining portion might not be significant enough to exist as a standalone article. Saligron 05:32, 30 January 2007 (UTC)

Alternating Tensor
I was redirected here form "alternating tensor", but I was looking for a definition of the alternating tensor which is the tensor density whose components are the signature of the indices as a permutation. It is anti-symmetric over all its indices. It should be mentioned somewhere, if not on its own then here, or under exterior algebras or tensor densities. I am not sure where would be best. Weburbia (talk) 17:59, 19 January 2008 (UTC)

Definitely this page should contain a description of the (unique up to normalization) completely antisymmetric tensor of order n in dimension n, i.e., as written above, the signature of the permutation formed by the indices. — Preceding unsigned comment added by 134.157.10.42 (talk) 14:02, 28 October 2014 (UTC)


 * The Riemannian volume form is mentioned, though perhaps this property should be mentioned? —Quondum 19:02, 28 October 2014 (UTC)