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Positive Semi-Definite Matrices
The present chapter deals essentially with positive semi-definite matrices. It is the longest chapter of the book, but the reader should be aware...
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Minima of Positive Definite Quadratic Forms
In Chapter 2 we defined Hermite’s constant \(\gamma _n\) ,...
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Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems
Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two...
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Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: the asymptotic approach
We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite...
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On the Structure of Conditionally Positive Definite Algebraic Operators
Recently, the authors have introduced and intensively studied a class of bounded Hilbert space operators called conditionally positive definite. Its...
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Infinite-dimensional distances and divergences between positive definite operators, Gaussian measures, and Gaussian processes
This paper presents a survey of recent results on the generalization of distances and divergences on the set of symmetric, positive definite (SPD)...
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Near order and metric-like functions on the cone of positive definite matrices
In this article we introduce a new relation on the cone of positive definite matrices and we study its properties and its effect on operator...
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A modified improved alternating positive semi-definite splitting preconditioner for double saddle point problems
In this paper, to further enhance the efficiency of the improved alternating positive semi-definite splitting (IAPSS) preconditioner proposed by Ren...
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On a Nontrivial Situation Concerning the Pseudounitary Eigenvalues of a Positive Definite Matrix
Let I p,q = I p ⊕− I q . Pseudounitary eigenvalues of a positive definite matrix A are the moduli of conventional eigenvalues of the matrix I p,q A . They...
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A Theta Function Attached to a Positive Definite Matrix
In the initial sections that are presented the purpose is to attach to a symmetric, positive definite,...
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On the Structure of Conditionally Positive Definite Algebraic Operators
Recently, the authors have introduced and intensively studied a class of bounded Hilbert space operators called conditionally positive definite. Its...
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Two-Variable Wasserstein Means of Positive Definite Operators
We investigate the two-variable Wasserstein mean of positive definite operators, as a unique positive solution of the nonlinear equation obtained...
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Entries of the inverses of large positive definite Toeplitz matrices
This is an expository paper embarking on the asymptotic behavior of the entries of the inverses of positive definite symmetric Toeplitz matrices as...
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Parameterized QHSS Iteration Method and Its Variants for Non-Hermitian Positive Definite Linear Systems of Strong Skew-Hermitian Parts
Based on the quasi-Hermitian and skew-Hermitian splitting (QHSS) iteration method proposed by Bai for solving the large sparse non-Hermitian positive...
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Bures–Wasserstein geometry for positive-definite Hermitian matrices and their trace-one subset
In his classical argument, Rao derives the Riemannian distance corresponding to the Fisher metric using a map** between the space of positive...
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A simplified relaxed alternating positive semi-definite splitting preconditioner for saddle point problems with three-by-three block structure
For solving the saddle point linear systems with three-by-three block structure, in this paper, based on the alternating positive semi-definite...
