Talk:Sylvester's law of inertia
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This isn't as clear as it might be. Nowhere is it said that A is a symmetric matrix. If A is symmetric one can get away with saying the eigenvalues of A are also its diagonal entries when thought of as a quadratic form. If not, then the quadratic form interpretation picks up only the symmetric part of A, throwing away the anti-symmetric part.
The simplest thing would be to clarify by making A symmetric at the outset.
Charles Matthews 09:37, 20 Apr 2005 (UTC)
[edit] much more general and without eigenvalues
Hello Sorry but i am always looking for more general definitions. On one hand this avoids confusion, on the other hand it becomes increasingly difficult to understand a simple case of something.
Anyway, the form of the law i use in my Symmetric bilinear form article, only uses ordered fields, and orthogonal basisses. Eigenvalues need not exist.
[edit] different theorem?
According to Horn and Johnson Thm 4.5.8, Sylvester's law of inertia says two Hermitian matrices A and B are unitarily similar iff they have the same inertia. If I'm not mistakened, what is here is trivial-- eigenvalues don't change under similarity transforms, so of course the inertia doesn't change. —The preceding unsigned comment was added by Swiftset (talk • contribs) 22:21, 5 March 2007 (UTC).
- I agree with this, and I'm going to change the statement of the theorem to one based on congruence transformations and emphasize the difference you pointed out. Akriasas 18:54, 6 October 2007 (UTC)
