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Uniqueness of size-2 positive semidefinite matrix factorizations
We characterize when a size-2 positive semidefinite (psd) factorization of a positive matrix of rank 3 and psd rank 2 is unique. The characterization is obtained using tools from rigidity theory. In the first step, we define s-infinitesimally rigid psd factorizations and characterize 1- and 2-infinitesimally rigid size-2 psd factorizations.
Dawson, Kristen +3 more
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From ƒ-Divergence to Quantum Quasi-Entropies and Their Use
Entropy, 2010 Csiszár’s ƒ-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting, positive semidefinite matrices are in the place of probability distributions and the quantum generalization is called ...
Dénes Petz
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Complexity of the Positive Semidefinite Matrix Completion Problem with a Rank Constraint [PDF]
, 2013 18 pages, 3 ...
Nagy, M., Laurent, M., Varvitsiotis, A.
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Positive Semidefinite Metric Learning with Boosting
, 2009 The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric.
Hengel, Anton van den +3 more
core
General Zagreb adjacency matrix [PDF]
Contributions to Mathematics, 2022 Zhen Lin
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Optimal Pilot Design for MIMO Broadcasting Systems Based on the Positive Definite Matrix Manifold
IEEE Access, 2019 In the MIMO broadcasting system, channel state information (CSI) is often used for data detection at the receiver or preprocessing techniques such as the power control and user scheduling at the transmitter and hence, the study of its acquisition is ...
Wen Zhou +4 more
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Positive semidefiniteness of estimated covariance matrices in linear models for sample survey data
Special Matrices, 2016 Descriptive analysis of sample survey data estimates means, totals and their variances in a design framework. When analysis is extended to linear models, the standard design-based method for regression parameters includes inverse selection probabilities ...
Haslett Stephen
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Semidefinite geometry of the numerical range
, 2008 The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI), an affine ...
Henrion, Didier
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A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots
International Journal of Mathematics and Mathematical Sciences, 2013 Following our paper [Linear Algebra Appl. 433(2010), 699–717], we present a framework and computational tools for the Coxeter spectral classification of finite posets J≡(J,⪯).
Daniel Simson, Katarzyna Zając
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Gaussian mixtures closest to a given measure via optimal transport
Comptes Rendus. MathématiqueGiven a determinate (multivariate) probability measure $\mu $, we characterize Gaussian mixtures $\nu _\phi $ which minimize the Wasserstein distance $W_2(\mu ,\nu _\phi )$ to $\mu $ when the mixing probability measure $\phi $ on the parameters $(\mathbf{
Lasserre, Jean B.
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