Title: Matrix inequalities in the Lowner ordering by means of Schur complement and block matrices

Authors: Cheng Zeng; Gantong He

Addresses: School of Science, Guizhou Institute of Technology, 550003, Guizhou, Guiyang, China ' College of Natural Science, Guizhou University, 550025, Guizhou, Guiyang, China

Abstract: It has been evident that a Schur complement plays an important role in many aspects of matrix theory, in statistics, as well as in applied mathematics. The purpose of this article is to present a family of matrix inequalities involving the Kronecker product, Hadamard product and ordinary sum. Our theorems contain or extend some existing known results.

Keywords: Schur complement; block matrix; Hadamard product; Kronecker product; Lowner ordering; matrix inequality; Moore-penrose inverse; Khatri-Rao product.

DOI: 10.1504/IJCSM.2018.091730

International Journal of Computing Science and Mathematics, 2018 Vol.9 No.2, pp.133 - 141

Accepted: 12 May 2017
Published online: 14 May 2018 *

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