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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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Norm inequalities for positive semidefinite matrices
Wuhan University Journal of Natural Sciences, 2012This paper aims to discuss some inequalities involving unitarily invariant norms and positive semidefinite matrices. By using properties of unitarily invariant norms, we obtain two inequities involving unitarily invariant norms and positive semidefinite matrices, which generalize the result obtained by Bhatia and Kittaneh.
Limin Zou, Yanqiu Wu
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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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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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Matrices with positive semidefinite real part
Linear and Multilinear Algebra, 2019Matrices with the property that the real part is positive definite, have been studied for the past five decades or more.
Choudhury, Projesh Nath, Sivakumar, KC
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A Measure Of Asymmetry For Positive Semidefinite Matrices
Optimization, 2003It is known that a continuous map is the gradient of a convex function if and only if it is cyclically monotone. Also, a differentiable map F is the gradient of a function if and only if the matrices F ′(x) are symmetric for all x in the domain. Based on this connection between symmetry and monotonicity, we define a measure of asymmetry for positive ...
Crouzeix, Jean-Pierre, Gutan, G.
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Completions of positive semidefinite operator matrices
2011This chapter deals with positive definite and semidefinite completions of partial operator matrices. It considers the banded case in Section 2.1, the chordal case in Section 2.2, the Toeplitz case in Section 2.3, and the generalized banded case and the operator-valued positive semidefinite chordal case in Section 2.6.
Mihály Bakonyi, Hugo J. Woerdeman
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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.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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