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

Given a $N\times K$ matrix $A$ of full rank with $ K < N $, a diagonal matrix $D$ and knowing that $E[D]=bI_N$, where $E[\cdot]$ is the expected value and $I_N$ is the $N\times N$ identity matrix and $b>0$ is a known scalar,

how can I compute (or bound): $E[\operatorname{trace}((A^H D A)^{-1} A^HA)]$

share|cite|improve this question

There is information missing in this question related to the assumptions of the matrix $D$. Consider for example the case of $D$=0 with probability 0.5, and $D=2bI_N$ with probability 0.5. This satisfies the assumption $E[D]=bI_N$, but the matrix inverse is undefined with probability 0.5.

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.