Results 31 to 40 of about 40,316 (199)

A counterexample to the Drury permanent conjecture

Special Matrices, 2017
We offer a counterexample to a conjecture concerning the permanent of positive semidefinite matrices. The counterexample is a 4 × 4 complex correlation matrix.
Hutchinson George
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Generic Spectrahedral Shadows [PDF]

, 2015
Spectrahedral shadows are projections of linear sections of the cone of positive semidefinite matrices. We characterize the polynomials that vanish on the boundaries of these convex sets when both the section and the projection are generic.Comment ...
Sinn, Rainer, Sturmfels, Bernd
core   +1 more source

Metric geometric means with arbitrary weights of positive definite matrices involving semi-tensor products

AIMS Mathematics, 2023
We extend the notion of classical metric geometric mean (MGM) for positive definite matrices of the same dimension to those of arbitrary dimensions, so that usual matrix products are replaced by semi-tensor products.
Arnon Ploymukda, Pattrawut Chansangiam
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Logarithmic barriers for sparse matrix cones

, 2012
Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with ...
Andersen, Martin S., Dahl, Joachim, Vandenberghe, Lieven   +2 more
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A new look at nonnegativity on closed sets and polynomial optimization [PDF]

, 2011
We first show that a continuous function f is nonnegative on a closed set $K\subseteq R^n$ if and only if (countably many) moment matrices of some signed measure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite (if $K$ is compact $\mu$
Lasserre, Jean B.
core   +3 more sources

A Characterization on Singular Value Inequalities of Matrices

Journal of Function Spaces, 2020
We obtain a characterization of pair matrices A and B of order n such that sjA≤sjB, j=1, …, n, where sjX denotes the j-th largest singular values of X. It can imply not only some well-known singular value inequalities for sums and direct sums of matrices
Wei Dai, Yongsheng Ye
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Hilbert’s 17th problem in free skew fields

Forum of Mathematics, Sigma, 2020
This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative ...
Jurij Volčič
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Measuring Sphericity in Positive Semi-Definite Matrices

Axioms
The measure of sphericity for positive semi-definite matrices plays a crucial role in understanding their geometric properties, especially in high-dimensional settings.
Dário Ferreira, Sandra S. Ferreira
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A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

, 2017
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model.
Cerf, N. J., Chakhmakhchyan, L., Garcia-Patron, R.   +2 more
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有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)

Zhejiang Daxue xuebao. Lixue ban, 2019
In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成), HENingxin(贺宁馨)   +1 more
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