Results 21 to 30 of about 5,647,728 (213)
Sparse Sums of Positive Semidefinite Matrices [PDF]
ACM Transactions on Algorithms, 2015 Many fast graph algorithms begin by preprocessing the graph to improve its sparsity. A common form of this is spectral sparsification, which involves removing and reweighting the edges of the graph while approximately preserving its spectral properties. This task has a more general linear algebraic formulation in terms of approximating sums of rank-one
Marcel Kenji de Carli Silva +2 more
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TRACE INEQUALITIES OF POSITIVE SEMIDEFINITE MATRICES [PDF]
, 2006 In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated. The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
ÖZEL, Mustafa +3 more
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Binary positive semidefinite matrices and associated integer polytopes [PDF]
, 2012 We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes.We begin by establishing some basic properties of these matrices and polytopes.
Sorensen, M M, Letchford, A N
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On a Parametrization of Positive Semidefinite Matrices with Zeros [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose nonedges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph.
Mathias Drton, Josephine Yu
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On Some Matrix Trace Inequalities
Journal of Inequalities and Applications, 2010 We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. Then, we obtain a trace inequality for products of two positive semidefinite block matrices by using 2×2 ...
Ramazan Türkmen +1 more
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A trace bound for integer-diagonal positive semidefinite matrices
Special Matrices, 2020 We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.
Mitchell Lon
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Separability for mixed states with operator Schmidt rank two [PDF]
Quantum, 2019 The operator Schmidt rank is the minimum number of terms required to express a state as a sum of elementary tensor factors. Here we provide a new proof of the fact that any bipartite mixed state with operator Schmidt rank two is separable, and can be ...
Gemma De las Cuevas +2 more
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Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices [PDF]
, 2020 This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite d × d matrices. In particular, for conservative and subcritical affine processes we show that a finite log-moment of the ...
Jonas Kremer +7 more
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Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations [PDF]
, 1991 Elsner L, Mehrmann V. Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations. Numerische Mathematik.
Mehrmann, Volker, Elsner, Ludwig
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An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices
Special Matrices, 2021 A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.
Hutchinson George
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