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http://dx.doi.org/10.14317/jami.2013.545

THE EXTREMAL RANKS AND INERTIAS OF THE LEAST SQUARES SOLUTIONS TO MATRIX EQUATION AX = B SUBJECT TO HERMITIAN CONSTRAINT

Dai, Lifang (School of Mathematics and Statistics, Tianshui Normal University)
Liang, Maolin (School of Mathematics and Statistics, Tianshui Normal University)

Publication Information

Journal of applied mathematics & informatics / v.31, no.3_4, 2013 , pp. 545-558 More about this Journal

Abstract

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

Keywords

Matrix equation; rank; inertia; Hermitian solution; least squares solution;

Citations & Related Records

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