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The Group-Algebraic Formalism of Quantum Probability and Its Applications in Quantum Statistical Mechanics. [PDF]

Entropy (Basel)
Gu Y, Wang J.
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The positive definite solution to a nonlinear matrix equation

Linear and Multilinear Algebra, 2016
In this paper, we consider a nonlinear matrix equation, which has the form , where is a positive integer, is an arbitrary complex matrix and is an Hermitian positive definite matrix. A double of elegant estimates of the Hermitian positive definite solution are obtained.
Jie Meng, Hyun-Min Kim
semanticscholar   +3 more sources

Multisplitting of a symmetric positive definite matrix

SIAM Journal on Matrix Analysis and Applications, 1990
Parallel iterative methods are studied, and the focus is on linear algebraic systems whose matrix is symmetric and positive definite. The set of unknowns may be viewed as a union of subsets of unknowns (possibly with overlap).
R. White
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Symmetric decomposition of a positive definite matrix [PDF]

Numerische Mathematik, 1965
R. Martin, G. Peters, J. H. Wilkinson
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Positive definite matrix functions on spheres defined by hypergeometric functions

Integral transforms and special functions, 2019
Positive definite matrix functions on spheres arise naturally in multivariate approximation and spatial statistics. The construction of strictly positive definite models has become one of the most important goals for the analysis and study of vector ...
J. Guella, V. Menegatto
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On Projection of a Positive Definite Matrix on a Cone of Nonnegative Definite Toeplitz Matrices

, 2018
We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness.
K. Filipiak, A. Markiewicz, Adam Mieldzioc, Aneta Sawikowska   +3 more
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SymNet: A Simple Symmetric Positive Definite Manifold Deep Learning Method for Image Set Classification

IEEE Transactions on Neural Networks and Learning Systems, 2021
By representing each image set as a nonsingular covariance matrix on the symmetric positive definite (SPD) manifold, visual classification with image sets has attracted much attention.
Rui Wang, Xiaojun Wu, J. Kittler
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On the Variation of the Determinant of a Positive Definite Matrix 1)

Indagationes Mathematicae (Proceedings), 1951
A. Ostrowski, O. Taussky
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Identification of a Positive Definite Mass Matrix

Journal of Vibration and Acoustics, 1988
In system identification it is important that any a priori information about the system is utilized in the processing of measured data. Structural vibration problems can be modelled in terms of mass, stiffness, and damping and it is usually the case that the mass matrix is positive definite.
Arthur W. Lees, John E. Mottershead, T. K. Tee   +2 more
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A positive-definite matrix which is not extendible [PDF]

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984
It has been noted that not all positive-semidefinite matrices are extendible in the multidimensional case. However, no example of such a matrix has been presented for a simple multidimensional analog of the one-dimensional time-series case. It is shown how such a matrix can be derived.
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