A system of k Sylvester-type quaternion matrix equations with 3k+1 variables

2020/07/29 by Qing‐Wen Wang, Wang, Qing-Wen, Mengyan Xie +1
Computer Science · Mathematics · #Matrix Theory and Algorithms #Algebraic and Geometric Analysis #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2007.14536

Abstract

In this paper, we provide some solvability conditions in terms of ranks for the existence of a general solution to a system of k Sylvester-type quaternion matrix equations with 3k+1 variables A_iX_i+Y_iB_i+C_iZ_iD_i+F_iZ_i+1G_i=E_i,~i=1,k. As applications of this system, we present rank equalities as the necessary and sufficient conditions for the existence of a general solution to some systems of quaternion matrix equations A_iX_i+(A_iX_i)_ϕ+C_iZ_i(C_i)_ϕ+F_iZ_i+1(F_i)_ϕ=E_i,~i=1,k.

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