Singular Values of Sums of Positive Semidefinite Matrices

被引:0
|
作者
CHEN Dongjun [1 ]
ZHANG Yun [1 ]
机构
[1] School of Mathematical Sciences, Huaibei Normal University
关键词
D O I
10.19823/j.cnki.1007-1202.2020.0035
中图分类号
O151.21 [矩阵论];
学科分类号
070104 ;
摘要
For positive real numbers a, b,■. In this note, we generalize this fact to matrices by proving that for positive semidefinite matrices A and B of order n, for any ■, where s;(X) denotes the j-th largest singular value of X and ■.This result sharpens some known result. Meanwhile, some related results are established.
引用
收藏
页码:307 / 310
页数:4
相关论文
共 50 条
  • [1] Singular values of differences of positive semidefinite matrices
    Zhan, XZ
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2000, 22 (03) : 819 - 823
  • [2] Sparse Sums of Positive Semidefinite Matrices
    De Carli Silva, Marcel K.
    Harvey, Nicholas J. A.
    Sato, Cristiane M.
    [J]. ACM TRANSACTIONS ON ALGORITHMS, 2016, 12 (01)
  • [3] SINGULAR VALUE INEQUALITIES FOR POSITIVE SEMIDEFINITE MATRICES
    Zou, L.
    Jiang, Y.
    [J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2014, 40 (03) : 631 - 638
  • [4] Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices
    Wang, Benju
    Zhang, Yun
    [J]. JOURNAL OF FUNCTION SPACES, 2021, 2021
  • [5] Singular value and norm inequalities for positive semidefinite matrices
    Al-Natoor, Ahmad
    Kittaneh, Fuad
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (19): : 4498 - 4507
  • [6] Singular value inequalities for convex functions of positive semidefinite matrices
    Al-Natoor, Ahmad
    Hirzallah, Omar
    Kittaneh, Fuad
    [J]. ANNALS OF FUNCTIONAL ANALYSIS, 2023, 14 (01)
  • [7] A note on properties of splittings of singular symmetric positive semidefinite matrices
    Zhi-Hao Cao
    [J]. Numerische Mathematik, 2001, 88 : 603 - 606
  • [8] A note on properties of splittings of singular symmetric positive semidefinite matrices
    Cao, ZH
    [J]. NUMERISCHE MATHEMATIK, 2001, 88 (04) : 603 - 606
  • [9] Singular value inequalities for convex functions of positive semidefinite matrices
    Ahmad Al-Natoor
    Omar Hirzallah
    Fuad Kittaneh
    [J]. Annals of Functional Analysis, 2023, 14
  • [10] Some results on traces of the generalized products and sums of positive semidefinite matrices
    Al-Mashaleh, Waseem
    Qawaqneh, Haitham
    Al-Zoubi, Hassan
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2022, 17 (02): : 619 - 625