Results 31 to 40 of about 2,871 (211)
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) +1 more
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, 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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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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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 +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 +3 more
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Trace-Inequalities and Matrix-Convex Functions
Fixed Point Theory and Applications, 2010 A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X↦f(X) via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of
Tsuyoshi Ando
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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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