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Fall Detection of Elderly People Using the Manifold of Positive Semidefinite Matrices [PDF]
Journal of Imaging, 2021 Falls are one of the most critical health care risks for elderly people, being, in some adverse circumstances, an indirect cause of death. Furthermore, demographic forecasts for the future show a growing elderly population worldwide.
Abdessamad Youssfi Alaoui +5 more
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Algorithms for positive semidefinite factorization [PDF]
Computational Optimization and Applications, 2018 21 pages, 3 figures, 3 ...
Arnaud Vandaele +2 more
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Polytopes of Minimum Positive Semidefinite Rank [PDF]
Discrete & Computational Geometry, 2013 The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals ...
Gouveia, João +2 more
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Affine Processes on Positive Semidefinite Matrices [PDF]
SSRN Electronic Journal, 2009 This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures ...
Cuchiero, Christa +3 more
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Positive semidefinite rank [PDF]
Mathematical Programming, 2015 Let M be a p-by-q matrix with nonnegative entries. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices $A_i, B_j$ of size $k \times k$ such that $M_{ij} = \text{trace}(A_i B_j)$. The psd rank has many appealing geometric interpretations, including semidefinite representations of ...
Gouveia, João +4 more
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Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces
Axioms, 2023 This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator A.
Najla Altwaijry +2 more
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On Some Matrix Trace Inequalities
Journal of Inequalities and Applications, 2010 We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. Then, we obtain a trace inequality for products of two positive semidefinite block matrices by using 2×2 ...
Ramazan Türkmen +1 more
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Mathematics, 2022 In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if and
Muhammad Faisal Iqbal, Faizan Ahmed
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Positive semidefinite univariate matrix polynomials [PDF]
Mathematische Zeitschrift, 2018 We study sum-of-squares representations of symmetric univariate real matrix polynomials that are positive semidefinite along the real line. We give a new proof of the fact that every positive semidefinite univariate matrix polynomial of size $n\times n$ can be written as a sum of squares $M=Q^TQ$, where $Q$ has size $(n+1)\times n$, which was recently ...
Hanselka, C., Sinn, R.
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Completely positive semidefinite rank [PDF]
Mathematical Programming, 2017 29 pages including appendix.
Prakash, Anupam +3 more
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