Eigenvalue equalities for ordinary and Hadamard products of powers of positive semidefinite matrices
نویسندگان
چکیده
منابع مشابه
Trace and Eigenvalue Inequalities for Ordinary and Hadamard Products of Positive Semidefinite Hermitian Matrices
Let A and B be n n positive semidefinite Hermitian matrices, let c and/ be real numbers, let o denote the Hadamard product of matrices, and let Ak denote any k )< k principal submatrix of A. The following trace and eigenvalue inequalities are shown: tr(AoB) <_tr(AoBa), c_<0or_> 1, tr(AoB)a_>tr(AaoBa), 0_a_ 1, A1/a(A o Ba) <_ Al/(Az o B), a <_ /,a O, Al/a[(Aa)k] <_ A1/[(A)k], a <_/,a/ 0. The equ...
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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 = (aij) be an n × n symmetric matrix with all positive entries and just one positive eigenvalue. Bapat proved then that the Hadamard inverse of A, given by A = ( 1 aij ) is positive semidefinite. We show that if moreover A is invertible then A is positive definite. We use this result to obtain a simple proof that with the same hypotheses on A, except that all the diagonal entries of A are...
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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: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.12.007