Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Take $n\ll N$. Let $P$ be an $n\times N$ matrix of iid $\mathcal{N}(0,1)$ random variables, and let $D$ be an $N\times N$ diagonal matrix.

What can be said about the distribution of the largest singular value of $PD$?

When $n=1$, I get concentration inequalities from Lemma 1 of this paper. I would like a probabilistic upper bound for the general case, and I wouldn't be surprised if this is already available in the literature.

share|improve this question
add comment

1 Answer

I think the following answers your question (and more): http://www-personal.umich.edu/~romanv/papers/product-random-deterministic.pdf

share|improve this answer
add comment

Your Answer

 
discard

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.