Talk:Skew-symmetric matrix

From Wikipedia, the free encyclopedia

The skew-symmetric n×n matrices form a vector space of dimension (n2 − n)/2. This is the tangent space to the orthogonal group O(n).

Shouldn't that say something like "the tangent space to the orthogonal group O(n) at the identity matrix"? Surely it's not the tangent space at all points. Josh Cherry 02:28, 12 Apr 2004 (UTC)

Yes, the tangent space at I. Charles Matthews 05:39, 12 Apr 2004 (UTC)

---

Skew-symmetric matrices fall into the category of normal matrices and are thus subject to the spectral theorem, which states that any real or complex skew-symmetric matrix can be diagonalized by a unitary matrix.

This statement appears incorrect; a complex skew-symmetric matrix is not necessarily normal, hence the spectral theorem may not apply. Is there something I am missing?

You're right. I added the requirement that the matrix be real. Thanks for mentioning it. -- Jitse Niesen (talk) 05:09, 12 June 2006 (UTC)