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Noncommutative symmetric functions with matrix parameters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices then
Alain Lascoux +2 more
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The symmetric M-matrix and symmetric inverse M-matrix completion problems
Linear Algebra and its Applications, 2002 AbstractThe symmetric M-matrix and symmetric M0-matrix completion problems are solved and results of Johnson and Smith [Linear Algebra Appl. 290 (1999) 193] are extended to solve the symmetric inverse M-matrix completion problem: (1)A pattern (i.e., a list of positions in an n×n matrix) has symmetric M-completion (i.e., every partial symmetric M-matrix
Leslie Hogben
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Modeling Tree-like Heterophily on Symmetric Matrix Manifolds [PDF]
EntropyTree-like structures, characterized by hierarchical relationships and power-law distributions, are prevalent in a multitude of real-world networks, ranging from social networks to citation networks and protein–protein interaction networks.
Yang Wu, Liang Hu, Juncheng Hu
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Symmetric Linearizations for Matrix Polynomials [PDF]
SIAM Journal on Matrix Analysis and Applications, 2006 A standard way of treating the polynomial eigenvalue problem $P(\lambda)x = 0$ is to convert it into an equivalent matrix pencil—a process known as linearization. Two vector spaces of pencils $\mathbb{L}_1(P)$ and $\mathbb{L}_2(P)$, and their intersection $\mathbb{DL}(P)$, have recently been defined and studied by Mackey, Mackey, Mehl, and Mehrmann ...
Nicholas J. Higham +3 more
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On the nonsingular symmetric factors of a real matrix
Linear Algebra and its Applications, 1974 AbstractFor a given real square matrix A this paper describes the following matrices: (∗) all nonsingular real symmetric (r.s.) matrices S such that A = S−1T for some symmetric matrix T.All the signatures (defined as the absolute value of the difference of the number of positive eigenvalues and the number of negative eigenvalues) possible for feasible ...
Frank Uhlig
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A complex associated with a symmetric matrix [PDF]
Kyoto Journal of Mathematics, 1977 Shirô Gotô, Sadao Tachibana
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Generalized Symmetric Neutrosophic Fuzzy Matrices [PDF]
Neutrosophic Sets and Systems, 2023 We develop the concept of range symmetric Neutrosophic Fuzzy Matrix and Kernel symmetric Neutrosophic Fuzzy Matrix analogous to that of an EP –matrix in the complex field. First we present equivalent characterizations of a range symmetric matrix and then
M. Anandhkumar +3 more
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Symmetric nonnegative matrix trifactorization
Linear Algebra and its Applications, 2023 The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $BCB^T$, where $C$ is a $k \times k$ symmetric matrix, and both $B$ and $C$ are required to be nonnegative.
Damjana Kokol Bukovšek, Helena Šmigoc
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Unfolding a symmetric matrix [PDF]
Journal of Classification, 1996 Graphical displays which show inter--sample distances are important for the interpretation and presentation of multivariate data. Except when the displays are two--dimensional, however, they are often difficult to visualize as a whole. A device, based on multidimensional unfolding, is described for presenting some intrinsically high-
John C. Gower +2 more
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Algorithms for solving a class of real quasi-symmetric Toeplitz linear systems and its applications
Electronic Research Archive, 2023 In this paper, fast numerical methods for solving the real quasi-symmetric Toeplitz linear system are studied in two stages. First, based on an order-reduction algorithm and the factorization of Toeplitz matrix inversion, a sequence of linear systems ...
Xing Zhang +3 more
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