Another Proof of a Singular Value Inequality Concerning Hadamard Products of Matrices

Abstract

Let A B denote the Hadamard product of A and B A B the same size complex matrices. let σ(A) denote the singular value vector of A. with components in decreasing order and let Mn (C) denote the space of all complex n×n matrices. This paper gives another proof of singular value inequality σ(A B)≺ω σ(A) σ(B) for any A B∈Mn (C), which has been obtained recently in {1, 3, 4, 7]