Results 31 to 40 of about 41,020 (249)
Semidefinite descriptions of the convex hull of rotation matrices [PDF]
, 2014 We study the convex hull of $SO(n)$, thought of as the set of $n\times n$ orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of $SO(n)$ is doubly spectrahedral, i.e. both it and its
Parrilo, Pablo A. +2 more
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Restricted Riemannian geometry for positive semidefinite matrices
Linear Algebra and its Applications, 2023 We introduce the manifold of {\it restricted} $n\times n$ positive semidefinite matrices of fixed rank $p$, denoted $S(n,p)^{*}$. The manifold itself is an open and dense submanifold of $S(n,p)$, the manifold of $n\times n$ positive semidefinite matrices of the same rank $p$, when both are viewed as manifolds in $\mathbb{R}^{n\times n}$.
A. Martina Neuman, Yuying Xie, Qiang Sun
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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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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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Positive Maps and Separable Matrices
, 2016 A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of positive ...
Nie, Jiawang, Zhang, Xinzhen
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A Unique "Nonnegative" Solution to an Underdetermined System: from Vectors to Matrices [PDF]
, 2009 This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems.
Ao Tang +3 more
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On cone of nonsymmetric positive semidefinite matrices
Linear Algebra and its Applications, 2010 AbstractIn this paper, we analyze and characterize the cone of nonsymmetric positive semidefinite matrices (NS-psd). Firstly, we study basic properties of the geometry of the NS-psd cone and show that it is a hyperbolic but not homogeneous cone. Secondly, we prove that the NS-psd cone is a maximal convex subcone of P0-matrix cone which is not convex ...
Yingnan Wang, Naihua Xiu, Jiye Han
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Measuring Sphericity in Positive Semi-Definite Matrices
AxiomsThe 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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The positive semidefiniteness of partitioned matrices
Linear Algebra and its Applications, 1988 AbstractThe positive semidefiniteness of a partitioned matrix is characterized in terms of its submatrices. The result is applied to a variety of problems concerning Löwner ordered matrices, which need not be partitioned themselves.
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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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