Singular value inequalities for convex functions of positive semidefinite matrices.

In this paper, we give new singular value inequalities for matrices. It is shown that if A, B, X are n × n matrices such that X is positive semidefinite, and if f : [ 0 , ∞) → R is an increasing nonnegative convex function, then s j f A X B ∗ X ≤ f A ∗ A + B ∗ B 2 X s j X <graphic href="43034_2022_233_Article_Equ23.gif"></graphic> and s j A X B ∗ ≤ 1 2 A ∗ A A 2 + B ∗ B B 2 A B s j X <graphic href="43034_2022_233_Article_Equ24.gif"></graphic> for j = 1 , 2 ,... , n . Some of our inequalities present refinements of some known singular value inequalities. [ABSTRACT FROM AUTHOR]