COSAM » Events » 2018 » February » DMS Linear Algebra/Algebra Seminar

 DMS Linear Algebra/Algebra Seminar Time: Feb 27, 2018 (04:00 PM) Location: Parker Hall 352 Details: Speaker: Zhuoheng He Title: The general $$\phi$$-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations Abstract: In this talk, we consider two systems of mixed pairs of quaternion matrix Sylvester equations $A_{1}X-YB_{1}=C_{1},~A_{2}Z-YB_{2}=C_{2}$ and $A_{1}X-YB_{1}=C_{1},~A_{2}Y-ZB_{2}=C_{2},$ where $$Z$$ is $$\phi$$-Hermitian. Some practical necessary and sufficient conditions for the existence of a solution $$(X,Y,Z)$$ to those systems in terms of the ranks and Moore-Penrose inverses of the given coefficient matrices will be presented. Moreover, the general solutions to these systems are explicitly given when they are solvable. We also provide some numerical examples to illustrate our results.

Last updated: 02/23/2018