学术报告

题      目：Singular Values, von Neumann Type Trace Inequality of Dual Quaternion Matrices, and Their Low-Rank Approximations

报  告  人：凌晨  教授  (邀请人：陈艳南 )

                                    杭州电子科技大学

时      间：9月12日  10：00-11：00

地     点：数科院东楼401

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。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。近十年来，主持国家自科基金和浙江省自科基金各4项、其中省基金重点项目1项。在国内外重要刊物发表论文80余篇，多篇发表在Math.Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等。

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.