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I want to read a proof of "Every quadratic form q in n variables over a field of characteristic not equal to 2 is equivalent to a diagonal form" using Gram-Schmidt orthogonalization. Could anyone suggets a reference to me?

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up vote 1 down vote accepted

I am pretty confident that Jacobson's Basic Algebra I covers reducing quadratic forms to diagonal form in chapter 6 Metric vector spaces and the classical groups.

I think I remember another proof, in less generality, in Tensor analysis on manifolds. I remember it was very readable and definitely used Gram-Schmidt.

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Thank you @rschwieb. I confirmed that both of two proofs you mentioned are indeed based on Gram-Schmidt. –  Aki Nov 10 '12 at 4:24
    
@Aki Happy to help! –  rschwieb Nov 10 '12 at 17:05
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