Results 1 to 10 of about 2,874 (210)
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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Trace inequalities for positive semidefinite matrices [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2017 Certain trace inequalities for positive definite matrices are generalized for positive semidefinite matrices using the notion of the group generalized inverse.
Choudhury Projesh Nath, Sivakumar K.C.
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Functions Operating on Positive Semidefinite Quaternionic Matrices [PDF]
Monatshefte Fur Mathematik, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Helge Glöckner
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Singular Values of Differences of Positive Semidefinite Matrices [PDF]
SIAM Journal on Matrix Analysis and Applications, 2001 Based on known results, the author shows relations between the singular values of two positive semidefinite matrices. Let \(A\) and \(B\) be complex positive semidefinite matrices of order \(n\) and let us denote as \(A \oplus B\) the block diagonal matrix with \(A\) and \(B\) on the diagonal. Using the common notation for singular values \(s_1(.) \geq
Xingzhi Zhan
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A trace bound for integer-diagonal positive semidefinite matrices
Special Matrices, 2020 We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.
Mitchell Lon
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On Positive Semidefinite Matrices with Known Null Space [PDF]
SIAM Journal on Matrix Analysis and Applications, 2002 We show how the zero structure of a basis of the null space of a positive semidefinite matrix can be exploited to determine a positive definite submatrix of maximal rank. We discuss consequences of this result for the solution of (constrained) linear systems and eigenvalue problems.
Zlatko Drmač, Peter Arbenz
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Low-rank matrix approximations over canonical subspaces
Journal of Numerical Analysis and Approximation Theory, 2020 In this paper we derive closed form expressions for the nearest rank-\(k\) matrix on canonical subspaces. We start by studying three kinds of subspaces. Let \(X\) and \(Y\) be a pair of given matrices. The first subspace contains all the \(m\times
Achiya Dax
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Sparse Sums of Positive Semidefinite Matrices [PDF]
ACM Transactions on Algorithms, 2015 Many fast graph algorithms begin by preprocessing the graph to improve its sparsity. A common form of this is spectral sparsification, which involves removing and reweighting the edges of the graph while approximately preserving its spectral properties. This task has a more general linear algebraic formulation in terms of approximating sums of rank-one
Marcel Kenji de Carli Silva +2 more
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On a Parametrization of Positive Semidefinite Matrices with Zeros [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph.
Mathias Drton, Josephine Yu
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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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