$$\eta $$-Hermitian Solution to a System of Quaternion Matrix Equations

Abstract

For $$\eta \in \{{\mathbf {i}},{\mathbf {j}},{\mathbf {k}}\}$$ , a real quaternion matrix A is said to be $$\eta $$ -Hermitian if $$A=A^{\eta *},$$ where $$A^{\eta *}=-\eta A^{*}\eta $$ , and $$A^{*}$$ stands for the conjugate transpose of A. In this paper, we present some practical necessary and sufficient conditions for the existence of an $$\eta $$ -Hermitian solution to a system of constrained two-sided coupled real quaternion matrix equations and provide the general $$\eta $$ -Hermitian solution to the system when it is solvable. Moreover, we present an algorithm and a numerical example to illustrate our results.