Eigenvalue majorization inequalities for positive semidefinite block matrices and their blocks
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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2 Let H = [ M K K∗ N ] be a Hermitian matrix. It is known that the eigenvalues of M ⊕N are 3 majorized by the eigenvalues of H . If, in addition, H is positive semidefinite and the block K 4 is Hermitian, then the following reverse majorization inequality holds for the eigenvalues: 5
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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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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.12.022