ON SOME SINGULAR VALUE INEQUALITIES FOR MATRICES

Abstract

Some singular value inequalities for matrices are given. Amongother inequalities it is proved that if f and g be nonnegative functions on[0, ∞) which are continuous and satisfying the relation f (t)g(t) = t, for allt ∈ [0, ∞), thensj ∗XB ∗XB ) 1≤ sj((A∗f(| X2(| X∗|)A+ A∗f2(| X∗|)A) ⊕ (B∗g2(| X |)B+ B∗g2(| X |)B)),2(| X 1(| X 2(| X 1+ Af(| X|)A2) ⊕ (Bg(| X |)B1+ Bg(| X |)B2)),for j = 1, 2, ..., n, where A1, A, B, B2, X are square matrices. Our results inthis article generalize some existing singular value inequalities of matrices

Keywords

• Singular values,Unitarily invariant norms; Positive semidefinite matrices; Positive definite matrices

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9. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China