Fractional Hadamard powers of positive semidefinite 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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X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.
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X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.
متن کاملTrace 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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00421-x