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Ranks of Hermitian and skew-Hermitian solutions to the matrix equation

โœ Scribed by Yonghui Liu; Yongge Tian; Yoshio Takane


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
192 KB
Volume
431
Category
Article
ISSN
0024-3795

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A simple representation of the general rank-constrained Hermitian nonnegative-definite (positive-definite) solution to the matrix equation AXA \* = B is derived. As medium steps, the general Hermitian solution and the general Hermitian nonnegative-definite (positive-definite) solution to the matrix

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In this paper, the Hermitian positive definite solutions of the matrix equation X s + A \* X -t A = Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers. Necessary and sufficient conditions for the existence of an Hermitian positive definite solution are