A Characterization on Singular Value Inequalities of Matrices. (18th February 2020) - Dai, Wei; Ye, Yongsheng
Abstract : We obtain a characterization of pair matrices A and B of order n such that s j A ≤ s j B, j = 1, …, n, where s j X denotes the j -th largest singular values of X . It can imply not only some well-known singular value inequalities for sums and direct sums of matrices but also Zhan's result related to singular values of differences of positive semidefinite matrices. In addition, some related and new inequalities are also obtained.