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2013 The solvability and the exact solution of a system of real quaternion matrix equations
Qing-Wen Wang , Xiang Zhang
Banach J. Math. Anal. 7(2): 208-224 (2013). DOI: 10.15352/bjma/1363784232

Abstract

In this paper, we establish necessary and sufficient conditions for the solvability of the system of real quaternion matrix equations $$ \left\{ \begin{array} {l}{A}_{1}X=C_{1},~ \\ YB_{1}=D_{1}, \\ A_{2}Z=C_{2},ZB_{2}=D_{2},A_{3}ZB_{3}=C_{3}, \\ A_{4}X+YB_{4}+C_{4}ZD_{4}=E_{1}. \end{array}\right. $$ We also present an expression of the general solution to the system. The findings of this paper widely extend the known results in the literature.

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Qing-Wen Wang . Xiang Zhang . "The solvability and the exact solution of a system of real quaternion matrix equations." Banach J. Math. Anal. 7 (2) 208 - 224, 2013. https://doi.org/10.15352/bjma/1363784232

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1263.15016
MathSciNet: MR3039948
Digital Object Identifier: 10.15352/bjma/1363784232

Subjects:
Primary: ‎15A24‎
Secondary: 47A06 , 47A50 , 47A62

Keywords: linear matrix equation , Moore-Penrose inverse , ‎rank‎

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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