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

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    杭州电子科技大学理学院教授

报告时间：2023年10月11日周三上午10:00

报告地点：S3-313

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.

个人简介：

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，主持国家自科基金和浙江省自科基金各多项。在Math. Program.、SIAM J. on Optim.、SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等国内外重要刊物发表论文多篇。