论文标题
$ k $ sylvester型四元基质方程的系统，$ 3K+1 $变量
A system of $k$ Sylvester-type quaternion matrix equations with $3k+1$ variables
论文作者
论文摘要
在本文中，我们提供了一些可解决性条件。美元作为该系统的应用，我们将等级平等作为存在的某些Quataternion矩阵方程系统的一般解决方案的必要条件美元f_ {i} z_ {i+1}（f_ {i}）_ ϕ = e_ {i}，〜i = \ edimline {1，k} $。
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 $A_{i}X_{i}+Y_{i}B_{i}+C_{i}Z_{i}D_{i}+F_{i}Z_{i+1}G_{i}=E_{i},~i=\overline{1,k}$. 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 $A_{i}X_{i}+(A_{i}X_{i})_ϕ+C_{i}Z_{i}(C_{i})_ϕ+F_{i}Z_{i+1}(F_{i})_ϕ=E_{i},~i=\overline{1,k}$.
