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

Qing-Wen Wang; Mengyan Xie

paper

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

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 $3 k + 1$ variables $A_{i} X_{i} + Y_{i} B_{i} + C_{i} Z_{i} D_{i} + F_{i} Z_{i + 1} G_{i} = E_{i}, i = 1, k$ . 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 $A_{i} X_{i} + (A_{i} X_{i})_{ϕ} + C_{i} Z_{i} (C_{i})_{ϕ} + F_{i} Z_{i + 1} (F_{i})_{ϕ} = E_{i}, i = 1, k$ .

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

Abstract

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