Results 191 to 200 of about 6,682,316 (219)

The unique square root of a positive semidefinite matrix

International Journal of Mathematical Education in Science and Technology, 2006
An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.
Koeber, Martin, Schäfer, Uwe
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Polynomial Instances of the Positive Semidefinite and Euclidean Distance Matrix Completion Problems [PDF]

SIAM Journal on Matrix Analysis and Applications, 2001
Summary: Given an undirected graph \(G=(V,E)\) with node set \(V=[1,n]\), a set \(S\subseteq V\), and a rational vector \(a\in \mathbb{Q}^{S\cup E}\), the positive semidefinite matrix completion problem consists of determining whether there exists a real symmetric \(n\times n\) positive semidefinite matrix \(X=(x_{ij})\) satisfying \(x_{ii}= a_i\) \((i\
Monique Laurent
exaly   +4 more sources

Completing a positive semidefinite matrix as a graph

IOSR Journal of Mathematics
This paper explores the completion of positive semidefinite (PSD) matrices through graph representation, emphasizing the fundamental properties of PSD matrices and their relevance in various applications, including statistics, machine learning, and optimization.
Hawa Ahmed Alrawayati, Ümit Tokeşer
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Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems

Journal of Global Optimization, 2003
This paper gives a variety of results on the Euclidean distance matrix completion problem, which is, if some entries of an \(n\times n\) matrix are specified, when can the rest of the matrix be filled in such that it is a matrix of distances between \(n\) points in some Euclidean space, and the related problem of completing a positive semidefinite ...
Hong-Xuan Huang, Zhian Liang, Panos M. Pardalos   +2 more
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On the uniqueness of positive semidefinite matrix solution under compressed observations

2010 IEEE International Symposium on Information Theory, 2010
In this paper, we investigate the uniqueness of positive semidefinite matrix solution to compressed linear observations. We show that under a necessary and sufficient condition for the linear compressed observations operator, there will be a unique positive semidefinite matrix solution to the compressed linear observations. It is further shown, through
Weiyu Xu, Ao Tang
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Positive semidefiniteness of $$D_{\alpha }$$-matrix on some families of graphs

Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gui-Xian Tian, Hui-Lu Sun, Shu-Yu Cui
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On the Controllability of Matrix Pairs $( A, K )$ with K Positive Semidefinite, II

SIAM Journal on Matrix Analysis and Applications, 1994
A famous result of \textit{C. T. Chen} [SIAM J. Appl. Math. 25, 158-161 (1973; Zbl 0273.15009)] and \textit{H. K. Wimmer} [Linear Algebra Appl. 8, 337-343 (1974; Zbl 0288.15015)] asserts that, if the matrix \(K = AH = HA^*\) is positive semidefinite and if \((A,K)\) is a controllable pair of matrices, then \(A\) has no eigenvalues on the imaginary line
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Fallacies in computational testing of matrix positive definiteness/semidefiniteness

IEEE Transactions on Aerospace and Electronic Systems, 1990
The status of computational tests for establishing matrix positive semidefiniteness and positive definiteness is reviewed. Two pervasive real-time tests that have been used for many years in varied applications to ensure that computed covariances encountered in Kalman filter applications are positive definite and discussed.
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Inequalities on 2 × 2 Block Positive Semidefinite Matrices

Linear and Multilinear Algebra, 2022
Pan-Shun Lau, Tin-Yau Tam, Xiaohui Fu
exaly  

Characterization of a Positive Semidefinite Matrix

Econometric Theory, 1992
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