Singular Values of Differences of Positive Semidefinite Matrices
نویسندگان
چکیده
منابع مشابه
Singular value inequalities for positive semidefinite matrices
In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].
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In this paper, we first give a lower and upper bounds for singular values of a 2×2 positive semidefinite block matrices. Then, we give some weakly majorization inequalities of singular values positive semidefinite block matrices. Also, we present inequalities involving the direct sum and sum of positive semidefinite matrices.
متن کاملsingular value inequalities for positive semidefinite matrices
in this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl. 308 (2000) 203-211] and [linear algebra appl. 428 (2008) 2177-2191].
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Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
متن کاملSingular Value Inequalities for Positive Semidefinite Matrices
In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2001
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479800369840