POSITIVE AND NEGATIVE DEFINITE SUBMATRICES IN AN HERMITIAN LEAST RANK SOLUTION OF THE MATRIX EQUATION AXA* = B

被引：1

作者：

Guerarra, Sihem ^{[1
]}

机构：

[1] Univ Oum El Bouaghi, Fac Exact Sci & Sci Nat & Life, Dept Math, Oum El Bouaghi 04000, Algeria

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2019年 / 9卷 / 01期

关键词：

Matrix equation; Moore-Penrose generalized inverse; Inertias; Least-rank solution;

D O I：

10.3934/naco.2019002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is devoted to establish the extremal inertias of the two submatrices X-1 and X-4 in a Hermitian least rank solution X of the matrix equation AXA* = B. From these formulas, necessary and sufficient conditions for these submatrices to be positive (nonpositive, negative, nonnegative) definite are achieved.

引用

页码：15 / 22

页数：8

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