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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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Unitarily invariant norm inequalities for positive semidefinite matrices
Linear Algebra and its Applications, 2021Ahmad Al-Natoor +2 more
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Comparison theorems for the minimum eigenvalue of a random positive-semidefinite matrix
arXiv.orgThis paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum eigenvalue of a ...
J. Tropp
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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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Positive semidefinite matrix supermartingales
Electronic Journal of ProbabilityWe explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices.
Hongjian Wang, Aaditya Ramdas
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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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International Conference on Geometric Science of Information, 2019
E. Massart, J. Hendrickx, P. Absil
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E. Massart, J. Hendrickx, P. Absil
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Norm inequalities for positive semidefinite matrices and a question of Bourin III
Positivity (Dordrecht), 2017M. Hayajneh +3 more
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