Results 41 to 50 of about 5,271,349 (211)

A New Algorithm for Positive Semidefinite Matrix Completion

Journal of Applied Mathematics, 2016
Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control.
Fangfang Xu, Peng Pan
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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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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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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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The positive semidefiniteness of partitioned matrices

Linear Algebra and its Applications, 1988
The author gives the character of the Löwner order, i.e. for symmetric matrices A and C such that \(C\leq A\), a symmetric matrix B satisfies \(C\leq B\leq A\) if and only if \(tr(R'B)\leq 1/2tr\{R'(A+C)\}+1/4tr(Q_ R)\) for all possible R, where \(Q_ R=\{(A-C)^{1/2}(R+R')(A-C)(R+R')(A- C)^{1/2}\}^{1/2}.\) An application to varieties of problems ...
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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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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 class of positive semidefinite matrices

Linear Algebra and its Applications, 1987
It is a known fact that, given a positive definite matrix \(y_{ij}\), the ``standardized'' matrix \(y_{ij}(y_{ii}y_{jj})^{-}\) is again positive definite. The authors investigate more general standardization methods of the form \(a_{ij}(\alpha)y_{ij}\) where \(\alpha\) is a positive number and \(a_{ij}(\alpha)=(\phi (x_ i,\alpha)+\phi (x_ j,\alpha))^{-}
Russell, A.M., Upton, C.J.F.
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Hyperbolic Relaxation of $k$-Locally Positive Semidefinite Matrices

SIAM Journal on Optimization, 2022
A successful computational approach for solving large-scale positive semidefinite (PSD) programs is to enforce PSD-ness on only a collection of submatrices. For our study, we let $\mathcal{S}^{n,k}$ be the convex cone of $n\times n$ symmetric matrices where all $k\times k$ principal submatrices are PSD.
Grigoriy Blekherman, Santanu S. Dey, Kevin Shu, Shengding Sun   +3 more
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Using distance on the Riemannian manifold to compare representations in brain and in models

NeuroImage, 2021
Representational similarity analysis (RSA) summarizes activity patterns for a set of experimental conditions into a matrix composed of pairwise comparisons between activity patterns.
Mahdiyar Shahbazi, Ali Shirali, Hamid Aghajan, Hamed Nili   +3 more
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