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Solving a class of quadratic matrix equations
Applied Mathematics Letters, 2018The authors describe all commuting solutions (i.e., \(AX=XA\)) and, under a full rank condition, all non-commuting solutions, of the matrix equation \(AXA=XAX\), for a given invertible matrix \(A\).
Saeed Ibrahim Adam Mansour +3 more
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An introduction to a class of matrix cone programming
Mathematical Programming, 2012A class of linear conic programming is defined (called matrix cone programming or MCP) involving the epigraphs of five commonly used matrix norms and the well studied symmetric cone. MCP has recently been found to have many important applications, for example, in nuclear norm relaxations of affine rank minimization problems. In order to make this class
Chao Ding, Defeng Sun, Kim-Chuan Toh
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A Combinatorial method for a class of matrix games
Journal of Applied Probability, 1966The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game.
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2006
A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance.
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A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance.
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A Class of Robustness Problems in Matrix Analysis
2002We present an overview of several results and a literature guide, prove some new results, and state open problems concerning description of all robust matrices in the following sense: Let be given a class of real or complex matrices A, and for each X ∈ A, a set G(X) is given.
Ran, A.C.M., Rodman, L.
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Research on a Class of Nonlinear Matrix Equation
2014In this paper, the nonlinear matrix equation \(X^{r}+\sum\limits_{i=1}^{m}A_{i}^{\ast}X^{\delta_{i}}A_{i}\) = Q is discussed. We propose the Newton iteration method for obtaining the Hermite positive definite solution of this equation. And a numerical example is given to identify the efficiency of the results obtained.
Jiating Fang +3 more
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On One Class of Matrix Differential Operators
Siberian Mathematical Journal, 2004The author continues the study of the isomorphic properties of partial differential operators in the special weighted Sobolev spaces \(W^l_{p,\sigma}\) introduced in his papers [Russ. Acad. Sci. Dokl., Math. 49, No. 1, 113--118 (1994; Zbl 0842.46016)] and [Boundary value problems for partial differential equations, Collect. sci. works, Novosibirsk 1986,
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Classes of submultiplicative matrix norms and their applications
TRU Mathematics, 1981Very often in numerical analysis, one needs a bound for a matrix, \(\| A\|\), where A is a square \(n\times n\) matrix. Bounding \(\| A\|\) depends upon a choice of matrix norms. We characterize certain classes of matrix norms whose bounds are controlled by the diagonal matrices, D, or components of a matrix A and give some applications to numerical ...
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On One Class of Matrix Topological *-Algebras
Ukrainian Mathematical Journal, 2001Let \(\Phi=\operatorname {pr} \lim _{\tau \in T}H_{\tau}\) be a projective limit of a family \((H_{tau})_{\tau \in T}\) of complex Hilbert spaces. The space \(\Phi\) is called nuclear if for each \(\tau \in T\) there exists \({\tau}'\in T\) such that the embedding \(H_{{\tau}'}\to H_{\tau}\) is quasi-nuclear.
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Multi-Class Fuzzy Support Matrix Machine for Classification in Roller Bearing Fault Diagnosis
Advanced Engineering Informatics, 2022Jinyu Tong, Haiyang Pan, Haifeng Xu
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