ON SOME SINGULAR VALUE INEQUALITIES FOR MATRICES

Authors : ILYAS ALI, Huyang, ABDULSHAKOOR

Pages : 58-89

View : 14 | Download : 11

Publication Date : 2014-06-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(t);ginsert ignore into journalissuearticles values(t); = t, for allt ∈ [0, ∞);, thensj ∗XB ∗XB ); 1≤ sjinsert ignore into journalissuearticles values(insert ignore into journalissuearticles values(A∗finsert ignore into journalissuearticles values(| X2insert ignore into journalissuearticles values(| X∗|);A+ A∗f2insert ignore into journalissuearticles values(| X∗|);A); ⊕ insert ignore into journalissuearticles values(B∗g2insert ignore into journalissuearticles values(| X |);B+ B∗g2insert ignore into journalissuearticles values(| X |);B););,2insert ignore into journalissuearticles values(| X 1insert ignore into journalissuearticles values(| X 2insert ignore into journalissuearticles values(| X 1+ Afinsert ignore into journalissuearticles values(| X|);A2); ⊕ insert ignore into journalissuearticles values(Bginsert ignore into journalissuearticles values(| X |);B1+ Bginsert ignore into journalissuearticles values(| 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