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arXiv · 2006.00189

Sylvester-type quaternion matrix equations with arbitrary equations and arbitrary unknowns

Zhuo-Heng He
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Abstract

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, $~i=\overline{1,k}$.

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Zhuo-Heng He. 2020-05-30. Sylvester-type quaternion matrix equations with arbitrary equations and arbitrary unknowns. https://arxiv.org/abs/2006.00189

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