A few months ago, while trying to show that the analysis in this paper is optimal (I discussed the paper in a past post), I was faced with the following question:

Given non-negative variance values that sum to , consider a random matrix whose entries are independent gaussians with mean zero and variance equal to . For which choice of is the expected value of the average singular value of that matrix maximized?

Continue reading The Lowner-Heinz Theorem and a simple result that should have a simpler proof