MathOverflow is a question and answer site for professional mathematicians. 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

we know a square matrix is similar to its transpose, this result holds true over any field. for they have the same "invariant factors".

Similarly, it has been proven that a square matrix is congruent to its transpose too. but the known proof of this result needs highly convoluted math. I wonder whether there is also something invariant under congruence or not. And with this we can give an elementary proof of this result.

for a proof of "A square matrix is congruent to its transpose"

see link text

share|cite|improve this question
why are you not happy with the proof in the link? – Martin Brandenburg Apr 16 '10 at 12:20
I think the proof by R.Horn et al has been very nice and concise. I read the paper many times and also wishes to simplify the proof, but at last, I accept the proof as the best one. – Sunni Apr 16 '10 at 15:25

Your Answer


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

Browse other questions tagged or ask your own question.