ON SOME SINGULAR VALUE INEQUALITIES FOR MATRICES

Year 2014, Volume: 2 Issue: 1, 58 - 89, 01.06.2014

ILYAS Alı Huyang ABDULSHAKOOR

https://izlik.org/JA77EA63GK

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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