# American Institute of Mathematical Sciences

March  2019, 9(1): 15-22. doi: 10.3934/naco.2019002

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

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

* Corresponding author: Sihem Guerarra

Received  September 2017 Revised  April 2018 Published  October 2018

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.

Citation: Sihem Guerarra. Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation AXA*=B. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 15-22. doi: 10.3934/naco.2019002
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