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.