Results 181 to 190 of about 5,271,349 (211)
Transformation of non positive semidefinite correlation matrices
Communications in Statistics - Theory and Methods, 1993 In multivariate statistics, estimation of the covariance or correlation matrix is of crucial importance. Computational and other arguments often lead to the use of coordinate-dependent estimators, yielding matrices that are symmetric but not positive semidefinite.
Rousseeuw, P.J., Molenberghs, G.
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Remarks on a Question of Bourin for Positive Semidefinite Matrices
Results in Mathematics, 2023For positive semidefinite matrices \(A\) and \(B\) over the field of complex numbers, the authors prove the norm inequalities \[ |||A^tB^{1-t}+B^tA^{1-t}|||\leq 2^{2(t-3/4)}|||A+B||| , \] if \(t\in [3/4,1]\) and \[ |||A^tB^{1-t}+B^tA^{1-t}|||\leq 2^{2(1/4-t)}|||A+B||| , \] if \(t\in [0,1/4].\) Here, \(|||\cdot |||\) is any unitarily invariant norm.
Hayajneh, Mostafa +2 more
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Positive Semidefinite Matrices
2018Positive semidefinite (PSD) and positive definite (PD) matrices are closely connected with Euclidean distance matrices. Accordingly, they play a central role in this monograph. This chapter reviews some of the basic results concerning these matrices.
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Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices
SIAM Journal on Optimization, 2003Summary: We build upon the work of \textit{M. Fukuda} et al. [SIAM J. Optim. 11, 647--674 (2001; Zbl 1010.90053)] and \textit{K. Nakata} et al. [Math. Program. 95, No. 2(B), 303--327 (2003; Zbl 1030.90081)], in which the theory of partial positive semidefinite matrices was applied to the semidefinite programming (SDP) problem as a technique for ...
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Positive Semidefinite Matrices
1999This chapter studies the positive semidefinite matrices, concentrating primarily on the inequalities of this type of matrix. The main goal is to present the fundamental results and show some often-used techniques. Section 7.1 gives the basic properties, Section 7.2 treats the L¨owner partial ordering of positive semidefinite matrices, and Section 7.3 ...
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A new Farkas lemma for positive semidefinite matrices
IEEE Transactions on Automatic Control, 1995Let \(A\) be a linear mapping of the vector space of symmetric real matrices of a given size. Let \(S\) be a closed convex cone of positive matrices. The Farkas lemma characterizes the consistency of the system \(Ax= b\), \(x\in S\). The author obtains a variant that avoids the closeness assumption imposed on \(S+ \ker A\).
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Neural Computation, 2009
The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods.
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The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods.
openaire +3 more sources