MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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 $V=\mathbb C^n$ be a vector space with (linear) maps $P_1:V\rightarrow V$ and $P_2:V\rightarrow V$ that are projectors , i.e. they satisfy $P_i^2=P_i$.

It is not hard to understand the structure of such a pair. One could see that $P_i$'s can be simultaneously block diagonalized with blocks of size $2$. For this see, and also for example paper of Halmos with the title "two subspaces".

My question is about a generalization of this to pairs of $P_1, P_2$ where $P_i$'s satisfy a different (simple) algebraic relation say $P_i^3= P_i$.

I want to see whether they can be block-digonalized with blocks of size $O(1)$ independent of $n$.

share|cite|improve this question

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.