SOLVING THE MATRIX INEQUALITY AXB plus (AXB)* >= C

Tian, Yongge; Von Rosen, Dietrich

doi:10.7153/mia-15-47

Abstract

A pair of complex Hermitian matrices A and B of the same size are said to satisfy an inequality A >= B in the Lowner partial ordering if A-B is nonnegative definite. In this note, we first derive the general solutions in closed-form for the linear matrix equation AXB + (AXB)* = C by using generalized inverses of matrices, and then derive general solutions of the linear matrix inequality AXB + (AXB)* >= C when C is a Hermitian nonnegative definite matrix.

Keywords

Linear matrix equation; linear matrix inequality; Lowner partial ordering; general solution; generalized inverses of matrices; rank; inertia

Published in

Mathematical Inequalities and Applications
2012, volume: 15, number: 3, pages: 537-548
Publisher: ELEMENT

SLU Authors

von Rosen, Dietrich
- Department of Energy and Technology, Swedish University of Agricultural Sciences

UKÄ Subject classification

Algebra and Logic

Publication identifier

DOI: https://doi.org/10.7153/mia-15-47

Permanent link to this page (URI)

https://res.slu.se/id/publ/45204