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

Do there exist results concerning preservation or not of the Morse index of a symmetric matrix $A$, after permuting its diagonal entries, and keeping fixed the off--diagonal ones?


share|cite|improve this question
up vote 1 down vote accepted

You can see that the signature is not preserved by this operation considering a matrix $A$ which is a direct sum of two matrices respectively of orders 2 and 1. Say that the off-diagonal entries are all zero but $a_{12}=a_{21}=1$.For instance, it is definite positive iff $a_{11}+a_{22} > 0$ $a_{11}a_{22} > 1,$ and $a_{33} > 0$, a condition which is in general not preserved by a permutation of the diagonal.

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.