A unified treatment for the restricted solutions of the matrix equation $AXB=C

In this paper, the Hermitian, skew-Hermitian, Re-nonnegative definite, Re-positive definite, Re-nonnegative definite least-rank and Re-positive definite least-rank solutions of the matrix equation $AXB= C$ are considered. The necessary and sufficient condition for the existence of such type of solut...

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Published inAIMS mathematics Vol. 5; no. 6; pp. 6594 - 6608
Main Authors Xu, Jiao, Zhang, Hairui, Liu, Lina, Zhang, Huiting, Yuan, Yongxin
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
hermitian (skew-hermitian) solution
matrix equation
re-nonnegative (re-positive) definite least-rank solution
re-nonnegative (re-positive) definite solution
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Summary:In this paper, the Hermitian, skew-Hermitian, Re-nonnegative definite, Re-positive definite, Re-nonnegative definite least-rank and Re-positive definite least-rank solutions of the matrix equation $AXB= C$ are considered. The necessary and sufficient condition for the existence of such type of solution to the equation is provided and the explicit expression of the general solution is also given.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020424