Solvability of systems of linear matrix equations subject to a matrix inequality

In this paper, the solvability conditions and the explicit expressions of the Hermitian solutions to the system of matrix equations and the Hermitian nonnegative definite solutions to the system of matrix equations are, respectively, put forward, by making full use of the generalized inverse and the...

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Vydáno v:Linear & multilinear algebra Ročník 64; číslo 12; s. 2446 - 2462
Hlavní autoři: Yu, Juan, Shen, Shu-qian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 01.12.2016
Taylor & Francis Ltd
Témata:
Algebra
Decision analysis
Formulas (mathematics)
Generalized inverse
Hermitian matrix
Hermitian nonnegative definite matrix
Inequalities
Inequality
Inertia
Mathematical analysis
Matrices (mathematics)
matrix equation
matrix inequality
Matrix methods
rank
Recursive algorithms
ISSN:0308-1087, 1563-5139
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Shrnutí:In this paper, the solvability conditions and the explicit expressions of the Hermitian solutions to the system of matrix equations and the Hermitian nonnegative definite solutions to the system of matrix equations are, respectively, put forward, by making full use of the generalized inverse and the rank of matrices. As applications, some special cases of the above systems of matrix equations are considered. In addition, the maximal ranks and inertias of the Hermitian solutions are, respectively, presented.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2016.1160998