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Strongly convex matrix functions
In this article, we study strongly convex matrix functions and the strong Davis-Sherman condition to see their relations, corresponding to those of...
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Fiedler Linearizations of Rectangular Rational Matrix Functions
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational...
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Singular values inequalities via matrix monotone functions
This paper uses matrix monotone functions as a key tool to obtain several relations among the singular values of certain celebrated matrix...
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Classification of Measurable Functions of Several Variables and Matrix Distributions
AbstractWe consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, this is an...
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A Low-Rank Matrix Approach to Compute Polynomial Approximations of Smooth Two-Dimensional Functions
Polynomial approximation of smooth functions is becoming increasingly important in fields like numerical analysis and scientific computing. These...
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Factorization of a Class of Matrix Functions in the Wiener Algebra of Order 2
AbstractA representative class of matrix functions from the Wiener algebra of order 2 admitting an effective factorization is found. The...
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Σ -Functions of the Categories of Matrix Representations of Nilpotent Semigroups
We study the categories of matrix representations of nilpotent semigroups over an arbitrary field. Our main attention is given to the Auslander...
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Vector Random Fields on the Probability Simplex with Metric-Dependent Covariance Matrix Functions
This paper constructs a class of isotropic vector random fields on the probability simplex via infinite series expansions involving the...
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Criteria and characterizations for spatially isotropic and temporally symmetric matrix-valued covariance functions
We consider spatial matrix-valued isotropic covariance functions in Euclidean spaces and provide a very short proof of a celebrated characterization...
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A Fast Monte Carlo Algorithm for Evaluating Matrix Functions with Application in Complex Networks
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix...
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Accretive Matrices and Matrix Convex Functions
In this paper, we present new inequalities for accretive matrices when treated via matrix convex and matrix monotone decreasing functions; as a new...
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Do the Mittag–Leffler Functions Preserve the Properties of Their Matrix Arguments?
The matrix Mittag–Leffler (ML) functions are receiving great attention at the moment. As a matter of fact, in many applications, the matrix argument...
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Completeness Theorems and Characteristic Matrix Functions Applications to Integral and Differential Operators
This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized eigenvectors of...
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Realizations of Non-commutative Rational Functions Around a Matrix Centre, II: The Lost-Abbey Conditions
In a previous paper the authors generalized classical results on minimal realizations of non-commutative (nc) rational functions, using nc...
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Matrix Inequalities and Characterizations of Operator Monotone Functions
In this chapter, we give a series of new characterizations of operator monotone functions using matrix inequalities involving different Kubo-Ando...
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A Class of Hölder Matrix Functions of the Second Order Admitting Effective Factorization
AbstractHölder matrix functions of the second order are considered. We assume that one element is arbitrary, diagonal elements do not vanish on the...
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On a Factorization Method for Matrix Functions in the Wiener Algebra of Order 2
AbstractA method for reducing the factorization problem for an arbitrary matrix function with nonnegative total index in (an everywhere dense...