Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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.

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.