报告题目：Singular Values, von Neumann Type Trace Inequality of Dual Quaternion Matrices, and Their Low-Rank Approximations

报告人：凌晨（杭州电子科技大学）

报告时间：2024年4月25日10:30--

报告地点：数统学院312报告厅

邀请单位：bat365在线登录入口

报告内容简介：

In this talk, we study some basic properties of dual quaternion matrices, which including singular values, polar decomposition, (appreciable) rank equalities and inequalities, the Courant-Fischer minimax principle, trace, and Weyl type monotonicity inequality. We extend the well-known von Neumann trace inequality for general dual quaternion matrices. Using the proposed trace inequality, we further obtain a Hoffman-Wielandt type inequality. We also propose two variants of the above two inequalities expressed by eigenvalues of dual quaternion Hermitian matrices, and establish an Eckart-Young type low-rank approximation theorem and reverse Eckart-Young Theorem.

报告人简介：

凌晨，杭州电子科技大学理学院教授，博士生导师。曾任中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长、中国运筹学会理事、中国系统工程学会理事、浙江省数学会常务理事等。现任国际期刊Pacific Journal of Optimization编委、Statistics, Optimization & Information Computing编委。近十余年来，连续主持国家自科基金和浙江省自科基金各4项(其中含省基金重点项目1项)。在Math. Program.、SIAM J. on Optim.和SIAM J. on Matrix Anal. and Appl.、COAP、JOTA、JOGO等国内外重要刊物发表论文多篇。