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学术报告109:Zhang Yang — A System of Matrix Equations over the Quaternion Algebra with Applications

时间:2022-10-21 作者: 点击数:

报告时间2022112日(星期三)8:30-9:30

报告地点腾讯会议 980-205-047

Zhang Yang 教授

工作单位:加拿大曼尼托巴大学

举办单位:学院

报告人简介:张扬教授,1965年出生河南省开封市,获得加拿大西安大略大学获得博士学位。目前为加拿大曼尼托巴大学教授。主要研究方向是环理论,计算机代数,自动推理证明,矩阵和张量理论, 包括斜多项式分解,Groebner 基理论,求解矩阵和张量方程,至今,张扬教授已在《Automatica》,《Linear Algebra and its Applications,Linear and Multilinear Algebra,Electronic Journal of Linear Algebra,Algebra Colloquium 等期刊上发表论文80余篇。他的研究得到了加拿大国家自然科学和工程基金 (NSERC) 连续支持,多次获得加拿大国家自然科学和工程基金。至今,张扬教授是加拿大国家自然科学和工程基金 (NSERC)评议委员会成员。  

报告简介 We give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations A(1)X(1) = C-1, AX(1)B(1) + X2B2 = C-3, A(2)X(2) + A(3)X(3)B = C-2 and X3B3 = C-4 over the quaternion algebra H, and present an expression of the general solution to this system when it is solvable. Using the results, we give some necessary and sufficient conditions for the system of matrix equations AX = C, X B = C over H to have a reducible solution as well as the representation of such solution to the system when the consistency conditions are met. A numerical example is also given to illustrate our results. As another application, we give the necessary and sufficient conditions for two associated electronic networks to have the same branch current and branch voltage and give the expressions of the same branch current and branch voltage when the conditions are satisfied.


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