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Congruences and Unitary Congruences in Matrix Theory
This paper is a review of basic facts related to important matrix transformations such as congruence, pseudo-similarity, and unitary congruence. We...
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On the Fundamental Solution Matrix of the Plane Anisotropic Elasticity Theory
AbstractAn explicit expression (in polar coordinates) for the fundamental solution matrix of the Lamé system of the plane anisotropic theory of...
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The Matrix Sequential Probability Ratio Test and Multivariate Ruin Theory
The matrix sequential probability ratio test (MSPRT) is a statistical method to decide which law governs a collection of independent and identically...
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Recent Developments of Fuzzy Matrix Theory and Applications
This book provides a comprehensive overview of the development of fuzzy matrix theory from its inception to its current state. It covers various...
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Matrix Inequalities in the Stability Theory: New Results Based on the Convolution Theorem
AbstractUsing Pyatnitskiy’s convolution theorem, the circle criterion of absolute stability for Lurie systems with several nonlinearities is obtained...
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Matrix and Operator Equations and Applications
This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and...
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Standard Forms of the Matrices Over Rings with Respect to Various Types of Equivalence and Their Applications to the Theory of Matrix Factorization and Matrix Equations
We present a survey of the results of investigations of one of the fields dealing with the equivalence of matrices originated by P. S. Kazimirs’kii...
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Random Matrix Theory
For the most part, the preceding chapters dealt with large sample techniques under the traditional asymptotic framework, that is, the sample size...
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Uniqueness of the Solution of Boundary Value Problems for the Static Equations of Elasticity Theory with a Nonsymmetric Matrix of Elastic Moduli
AbstractWe prove the uniqueness of a solution of boundary value problems for the static equations of elasticity theory for Cauchy elastic materials...
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A computational framework for connection matrix theory
The connection matrix is a powerful algebraic topological tool from Conley index theory, a subfield of topological dynamics. Conley index theory is a...
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Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory
This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds...
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Neutrosophic Matrix and Neutrosophic Fuzzy Matrix
After the development of the fuzzy set (FS) theory, many problems with non-random uncertainty are tackled using this theory. While solving these...
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Matrix Equations
This chapter concentrates on solving the matrix equation $$\textbf{A}\textbf{x} =...
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Simplifying matrix differential equations with general coefficients
We show that the n × n matrix differential equation δ ( Y ) = AY with n 2 general coefficients cannot be simplified to an equation in less than n ...
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Solving Linear Systems by Matrix Theory
In this chapter, we review basic results about finite-dimensional complex vector spaces, and the eigenvectors and eigenvalues of finite square...
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Iterative methods based on low-rank matrix for solving the Yang–Baxter-like matrix equation
We propose an effective matrix iteration method and a novel zeroing neural network (NZNN) model for finding numerical commuting solutions of the...
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Matrix Approximation by a Sum of Matrix Products
In this paper, we consider solutions of the problems related to the modelling of data transmission systems. Mathematically, the problem is formulated...
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Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces
In this paper, considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural...
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Explicit Formulas for the Matrix Logarithm and the Principal Matrix Logarithm
AbstractWe present new closed-form formulas for the matrix logarithm. Our method is direct and elementary, and it gives tractable and manageable...
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Dilation theory in finite dimensions and matrix convexity
We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This...