Inequalities involving Hadamard products of positive semidefinite matrices (Q1974238)

This paper is an extension of two inequalities. An inequality established by \textit{G. P. H. Styan} [Linear Algebra Appl. 6, 217-240 (1973; Zbl 0255.15002)] is on the Hadamard product and a correlation matrix. An inequality obtained by \textit{B. Wang} and \textit{F. Zhang} [Linear Multilinear Algebra 43, No. 1-3, 315-326 (1997; Zbl 0893.15008)] involves the Hadamard product and Schur complements. These two inequalities hold in the positive definite matrix case. Based on Albert's theorem, the author presents their extensions to cover the positive semidefinite matrix case. The relevant inequalities are also given. The main results are in Section 2.