Hadamard powers and totally positive matrices
نویسندگان
چکیده
منابع مشابه
On Fractional Hadamard Powers of Positive Block Matrices
Entrywise powers of matrices have been well-studied in the literature, and have recently received renewed attention due to their application in the regularization of highdimensional correlation matrices. In this paper, we study powers of positive semidefinite block matrices (Hst) n s,t=1 where each block Hst is a complex m × m matrix. We first characterize the powers α ∈ R such that the blockwi...
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The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Hig...
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Article history: Received 3 September 2013 Available online xxxx
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Let Sn be the positive real symmetric matrix of order n with (i, j ) entry equal to ( i + j − 2 j − 1 ) , and let x be a positive real number. Eigenvalues of the Hadamard (or entry wise) power S n are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S n are approximately equal to 4 4k−1 ( 2n− 2 n− 1 )k . © 2005 Elsevier Inc. All rights r...
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If/ is an irreducible character of Sn, these functions are known as immanants; if/ is an irreducible character of some subgroup G of Sn (extended trivially to all of Sn by defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of Sn, respectively. We should po...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.01.012