Luis Daniel Abreu proves the (complex version of) the Monotonicity of Singular Values Conjecture


The semester is under way and, as I announced here, I am teaching a new version of the Mathematics of Data Science course I taught last fall. As I go through the material, and the open problems, I will announce here in the blog progress that has been done on the open problems since I last gave the class.

I am very happy to announce that Luis Daniel Abreu posted a proof for the complex version of the Conjecture regarding the Monotonicity of the average Singular Value of a Gaussian Matrix (see the Conjecture here: , it is Open Problem 1.2 of last years version of the class: )

Luis Daniel Abreu was a mentor of mine back in my undergraduate times, and was my first co-author! The solution is available in the arxiv at:


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