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Research Article | Open Access

The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations A 1 X A 1 ∗ = C 1 and A 2 X A 2 ∗ = C 2

Yinlan Chen( ), Lina Liu
School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China
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Abstract

In this paper, we consider the common Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions to a pair of linear matrix equations A 1 X A 1 ∗ = C 1 , A 2 X A 2 ∗ = C 2 and present some necessary and sufficient conditions for their solvability as well as the explicit expressions for the general common Re-nnd and Re-pd solutions when the consistent conditions are satisfied.

Keywords

matrix equationRe-nonnegative definite solutionRe-positive definite solutionMoore-Penrose inversegeneralized singular value decomposition
CLC number: 15A24, 15A57

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 384-397
DOI: 10.3934/math.2022026

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Chen Y, Liu L. The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations A 1 X A 1 ∗ = C 1 and A 2 X A 2 ∗ = C 2 . AIMS Mathematics, 2022, 7(1): 384-397. https://doi.org/10.3934/math.2022026

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Received: 20 August 2021
Accepted: 06 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)