A system of real quaternion matrix equations with applications

By Qing-Wen Wang, J. Woude, Haixia Chang. 2009

136 citations recorded by the source corpus.

Abstract Let H be the real quaternion algebra and H n × m denote the set of all n × m matrices over H . Let P ∈ H n × n and Q ∈ H m × m be involutions, i.e., P 2 = I , Q 2 = I . A matrix A ∈ H n × m is said to be ( P , Q ) -symmetric if A = PAQ . This paper studies the system of linear real quaternion matrix equations A 1 X 1 = C 1 X 1 B 1 = C 2 A 2 X 2 = C 3 X 2 B 2 = C 4 A 3 X 1 B 3 + A 4 X 2 B 4 = C c . We present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied. As applications, we discuss the necessary and sufficient conditions for the system A a X = C a , XB b = C b , A c XB c = C c to have a ( P , Q ) -symmetric solution. We also show an expression of the ( P , Q ) -symmetric solution to the system when the solvability conditions are met. Moreover, we provide an algorithm and a numerical example to illustrate our results. The findings of this paper extend some known results in the literature.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1fcfde58d99f783bbd8439ac0bf1efb51f629f67

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In Algebra and Number Theory

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Some matrix equations with applications† (2012, background): “11–12, November–December 2012, 1327–1353 Some matrix equations with applicationsy Qing-Wen Wang* and Zhuo-Heng He Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China Communicated by F. Zhang (Received 31 July 2011; final version received 6 December 2011) We establish necessar”
The η-bihermitian solution to a system of real quaternion matrix equations (2014, background): “Moreover, a recent paper [23] by Wang et al.”
The general coupled matrix equations over generalized bisymmetric matrices (2010, background): “In the literature, the problem for determining a solution to several linearmatrix equations has been widely studied [10,14,22–24,27–30,33,35,43,44].”
The general solutions to some systems of matrix equations (2015, unknown): “[1–46]).”