Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation AXA*=B

Sihem Guerarra

doi:10.3934/naco.2019002

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2019, Volume 9, Issue 1: 15-22. Doi: 10.3934/naco.2019002

This issue Previous Article A brief survey of methods for solving nonlinear least-squares problems Next Article Stability preservation in Galerkin-type projection-based model order reduction

Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation AXA^*=B

Sihem Guerarra^,

Faculty of exact sciences and sciences of nature and life, Department of Mathematics, University of Oum El Bouaghi, 04000, Algeria

* Corresponding author: Sihem Guerarra
* Corresponding author: Sihem Guerarra

Received: August 31, 2017

Revised: March 31, 2018

Published: February 2019

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Abstract

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

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Mathematics Subject Classification: Primary: 15A24; Secondary: 15A03, 15A09, 15B57.

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