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