论文标题
带有任意方程和任意未知数的Sylvester型四基矩阵方程
Sylvester-type quaternion matrix equations with arbitrary equations and arbitrary unknowns
论文作者
论文摘要
在本文中，我们证明了一种猜想，该猜想是在最近的一篇论文中提出的[Linear Apla Appl。 2016; 496：549--593]。我们得出了一些实用的必要条件，以实现解决耦合双面Sylvester-type Quaternion矩阵方程的解决方案的解决方案，并具有任意方程式和任意未知数美元作为应用程序，我们给出了一些实用的必要条件，以使$η$ -Hermitian解决方案对quaternion矩阵方程式$ a_ {i} x_ {i} x_ {i} a^{η*} _ {η*} _ {i}+c_ {i}+c_ {i}等级，$ 〜I = \ edline {1，k} $。
In this paper, we prove a conjecture which was presented in a recent paper [Linear Algebra Appl. 2016; 496: 549--593]. We derive some practical necessary and sufficient conditions for the existence of a solution to a system of coupled two-sided Sylvester-type quaternion matrix equations with arbitrary equations and arbitrary unknowns $A_{i}X_{i}B_{i}+C_{i}X_{i+1}D_{i}=E_{i},~i=\overline{1,k}$. As an application, we give some practical necessary and sufficient conditions for the existence of an $η$-Hermitian solution to the system of quaternion matrix equations $A_{i}X_{i}A^{η*}_{i}+C_{i}X_{i+1}C^{η*}_{i}=E_{i}$ in terms of ranks, $~i=\overline{1,k}$.
