报告题目：Singular Values, von Neumann Type Trace Inequality of Dual Quaternion Matrices, and Their Low-Rank Approximations
报告人：杭州电子科技大学凌晨教授
报告时间：2023年9月27日下午4：00-5：00
报告地点：重庆工商大学数学与统计学院80602会议室
报告摘要：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。现任中国经济数学与管理数学研究会副理事长，曾任中国运筹学会数学规划分会副理事长、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。近十多年来，主持国家自然科学基金4项，浙江省自然科学基金4项、其中省重点项目1项。在国内外重要刊物例如Math. Program.、SIAM J. on Optim. 和SIAM J. on Matrix Anal. and Appl.、COAP、JOTA、JOGO等发表论文80余篇。
