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A New Algorithm for Positive Semidefinite Matrix Completion [PDF]
Journal of Applied Mathematics, 2016 Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and low-rank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control.
Fangfang Xu, Peng Pan
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Fall Detection of Elderly People Using the Manifold of Positive Semidefinite Matrices
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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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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Hilbert’s 17th problem in free skew fields
Forum of Mathematics, Sigma, 2020 This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative ...
Jurij Volčič
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The complete positivity of symmetric tridiagonal and pentadiagonal matrices
Special Matrices, 2022 We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix AA is completely positive. Our decomposition can be applied to a wide range of matrices.
Cao Lei, McLaren Darian, Plosker Sarah
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Analysis of Fixing Nodes Used in Generalized Inverse Computation
Advances in Electrical and Electronic Engineering, 2014 In various fields of numerical mathematics, there arises the need to compute a generalized inverse of a symmetric positive semidefinite matrix, for example in the solution of contact problems.
Pavla Hruskova
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Sufficient conditions to be exceptional
Special Matrices, 2016 A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A
Johnson Charles R., Reams Robert B.
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Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse
Special Matrices, 2020 A real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both ...
Das Joyentanuj +2 more
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A counterexample to the Drury permanent conjecture
Special Matrices, 2017 We offer a counterexample to a conjecture concerning the permanent of positive semidefinite matrices. The counterexample is a 4 × 4 complex correlation matrix.
Hutchinson George
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Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A
Abstract and Applied Analysis, 2013 We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X).
Dongjie Gao
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