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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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.
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A determinantal inequality for positive semidefinite matrices
, 2014 Minghua Lin
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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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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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Conditions for Existence of Dual Certificates in Rank-One Semidefinite Problems [PDF]
, 2014 Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate.
Hand, Paul
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Experimental Joint Estimation of Phase and Phase Diffusion Via Deterministic Bell Measurements
Advanced Science, EarlyView.This work employs Bell measurement, a form of entangling measurement, to estimate both the phase and its fluctuations in an optical interferometer. By incorporating a novel quantum effect at the measurement stage, the proposed method achieves the ultimate precision limit and demonstrates the significant potential of entangling measurements in multi ...
Ben Wang +4 more
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GBD and $ \mathcal{L} $-positive semidefinite elements in $ C^* $-algebras
AIMS MathematicsThis paper focused on the generalized Bott-Duffin (GBD) inverse and the $ {\rm GBD} $ elements in Banach algebra with involution and $ C^* $-algebra, as well as on the property of the $ p $-positive semidefinite elements that are a generalization of the $
Kezheng Zuo +2 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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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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