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Mat. Zametki, 2009, Volume 85, Issue 3, Pages 470–475 (Mi mz6632)  

This article is cited in 1 scientific paper (total in 1 paper)

On Hermitian Nonnegative-Definite Solutions to Matrix Equations

X.-Q. Liua, J.-Y. Rongb

a Huaiyin Institute of Technology
b Huaian College of Information Technology

Abstract: For a system of $q$ matrix equations denoted by
$$ \mathbf A_i\mathbf X\mathbf A_i^*=\mathbf B_i\mathbf B_i^*,\qquad i=1,2,…,q, $$
the problem of the existence of Hermitian nonnegative-definite solutions is considered in this note. We offer an alternative with simplification and regularity to the result on necessary and sufficient conditions for the above matrix equations with $q=2$ to have a Hermitian nonnegative-definite solution obtained by Zhang [1], who provided a revision of Young et al. [2]. Moreover, we give a necessary condition for the general case and then pose a conjecture, for which at least some special situations are argued.

Keywords: matrix equation, Hermitian nonnegative-definite solution, Hermitian matrix, Moore–Penrose inverse

DOI: https://doi.org/10.4213/mzm6632

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English version:
Mathematical Notes, 2009, 85:3, 453–457

Bibliographic databases:

UDC: 517.518.24+517.518.3
Received: 22.04.2007

Citation: X.-Q. Liu, J.-Y. Rong, “On Hermitian Nonnegative-Definite Solutions to Matrix Equations”, Mat. Zametki, 85:3 (2009), 470–475; Math. Notes, 85:3 (2009), 453–457

Citation in format AMSBIB
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\by X.-Q.~Liu, J.-Y.~Rong
\paper On Hermitian Nonnegative-Definite Solutions to Matrix Equations
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\pages 470--475
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\vol 85
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\pages 453--457
\crossref{https://doi.org/10.1134/S000143460903016X}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tian Yongge, “Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions”, Banach J. Math. Anal., 8:1 (2014), 148–178  crossref  mathscinet  zmath  isi  scopus
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