MATRIX SUBADDITIVITY INEQUALITIES AND BLOCK-MATRICES
نویسندگان
چکیده
منابع مشابه
Matrix Inequalities by Means of Block Matrices 1
One of the most useful tools for deriving matrix inequalities is to utilize block matrices; usually they are 2× 2 in most applications. In this paper, we shall show a weak log-majorization inequality of singular values for partitioned positive semidefinite matrices, from which some classical and recent results of Bhatia and Kittaneh [4], Wang, Xi and Zhang [12], and Zhan [13] will follow. We sh...
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Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities.
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Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities.
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This paper presents some results that complement (2). We believe our results are of new pattern concerning determinantal inequalities. Let us fix some notation. The matrices considered here have entries from the field of complex numbers. X ′,X ,X∗ stand for transpose, (entrywise)conjugate, conjugate transpose of X , respectively. For two n -square Hermitian matrices X ,Y , we write X > Y to mea...
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In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be uniformly approximated by roots of matrix orthogonal polynomials which were investigated independently from the random matrix literature. As a consequence we deriv...
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2009
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x09005509