Results 21 to 30 of about 1,468 (179)
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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Characterizing graphs with fully positive semidefinite Q-matrices
Linear Algebra and its Applications, 2023 6 ...
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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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Fractional Hadamard powers of positive semidefinite matrices
Linear Algebra and its Applications, 2003 The authors consider the class \(\varphi_n\) of all real positive semidefinite \(n\times n\) matrices, and the subclass \(\varphi^+_n\) of all \(A\in\varphi_n\) with non-negative entries. For a positive, non-integer number \(\alpha\) and some \(A\in \varphi_n^+\), when will the fractional Hadamard power \(A^{\diamondsuit \alpha}\) again belong to ...
Fischer, P., Stegeman, J.D.
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Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
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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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Matrices with high completely positive semidefinite rank
Linear Algebra and its Applications, 2017 A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite rank of $M$, and it is an open question whether there exists an upper bound on this number as a function of the ...
de Laat, David +2 more
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Enabling Stochastic Dynamic Games for Robotic Swarms
Advanced Intelligent Systems, EarlyView.This paper scales stochastic dynamic games to large swarms of robots through selective agent modeling and variable partial belief space planning. We formulate these games using a belief space variant of iterative Linear Quadratic Gaussian (iLQG). We scale to teams of 50 agents through selective modeling based on the estimated influence of agents ...
Kamran Vakil, Alyssa Pierson
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