ON SOME SINGULAR VALUE INEQUALITIES FOR MATRICES
ON SOME SINGULAR VALUE INEQUALITIES FOR MATRICES
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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- Kittaneh, F., Notes on some inequalities for Hilbert space operators, Res. Inst. Math. Sci. 24 (1988), 283-293.
- Zou, L. and Jiang, Y., Inequalities for unitarily invariant norms, J. Math. Inequal. 6 (2012), 279-287.
- Bhatia, R. and Kittaneh, F., On the singular values of a product of operators, SIAM J. Matrix Anal. Appl. 11 (1990), 272-277.
- Bhatia, R., Davis, C., More matrix forms of arithmetic-geometric mean inequality. SIAM J. Matrix Anal. Appl. 14 (1993), 132-136.
- Bhatia, R., Kittaneh, F., Notes on matrix arithmetic-geometric mean inequalities, Linear Algebra Appl. 308(2000) 203-211.
- Bhatia, R. and Kittaneh, F., The matrix arithmetic-geometric mean inequality revisited, Linear Algebra Appl. 428 (2008), 2177-2191.
- Audeh, W. and Kittaneh, F., Singular values inequalities for compact operators, Linear Algebra Appl. 437 (2012), 2516-2522.
- Tao, Y., More results on singular value inequalities of matrices, Linear Algebra Appl. 416 (2006), 724-729.
- College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2013
- Yayıncı: Mehmet Zeki SARIKAYA
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