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

Let M = P*D, where P is a permutation matrix and D diagonal. If P is also symmetric, then does M have all real eigenvalues?

share|cite|improve this question
up vote 5 down vote accepted

How about $M = \begin{pmatrix}0&1\\\1&0\end{pmatrix}\begin{pmatrix}-1&0\\\0&1\end{pmatrix}$?

share|cite|improve this answer

No. If $P$ is the matrix of a transposition (2 by 2) and $D$ is $diag(1, -1)$ the eigenvlues are imaginary.

share|cite|improve this answer

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.