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

I am looking at the matrices described in the title: matrices where all eigenvalues lie in the unit disc, and with the eigenvalues of modulus 1 having 1x1 Jordan blocks. My question is, is there a term for such matrices?

A related question is, since we lose the Jordan normal form in infinite dimensions, what is the appropriate infinite-dimensional analog of this condition (if there is one)?

share|cite|improve this question
You can call it a diagonalizable Schur matrix. – percusse Feb 9 '15 at 9:25

To the second question: You can check that your condition is equivalent to $$ \limsup_{n \to \infty} \|A^n \| \leq 1. $$ If there is an eigenvalue > 1, it is clear that the above fails. If an eigenvalue = 1 has non-trivial Jordan block, you have $\|A^n\| \gtrsim n$, so the condition is violated.

As for a name, in my opinion "subunitary" would seem appropriate. But that is just a guess and not based on knowledge.

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.