This article is cited in 2 papers

On Hermitian Nonnegative-Definite Solutions to Matrix Equations

X.-Q. Liu^a, J.-Y. Rong<sup>b

a</sup> Huaiyin Institute of Technology
^b Huaian College of Information Technology

Abstract: For a system of $q$ matrix equations denoted by
$$ \mathbf A_i\mathbf X\mathbf A_i^*=\mathbf B_i\mathbf B_i^*,\qquad i=1,2,\dots,q, $$
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.

UDC: 517.518.24+517.518.3

Received: 22.04.2007

DOI: 10.4213/mzm6632

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

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