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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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Cayley's hyperdeterminant, the principal minors of a symmetric matrix and the entropy region of 4 Gaussian random variables [PDF]
2008 46th Annual Allerton Conference on Communication, Control, and Computing, 2008 It has recently been shown that there is a connection between Cayley's hypdeterminant and the principal minors of a symmetric matrix. With an eye towards characterizing the entropy region of jointly Gaussian random variables, we obtain three new results ...
Sormeh Shadbakht, B. Hassibi
semanticscholar +5 more sources
Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix
Special Matrices, 2016 By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases.
Kurata Hiroshi, Bapat Ravindra B.
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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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The symmetric M-matrix and symmetric inverse M-matrix completion problems
Linear Algebra and its Applications, 2002 A partial matrix is a matrix in which some entries are specified and others are not. The completion problem for partial matrices consists in choosing values for the unspecified entries in such a way as the completed matrix belongs to a particular class of matrices. A partial \(n \times n\) matrix specifies a pattern (i.e.
Leslie Hogben
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Symmetric Linearizations for Matrix Polynomials [PDF]
SIAM Journal on Matrix Analysis and Applications, 2007 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 ...
Higham, Nicholas J. +3 more
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Polynomials compatible with a symmetric Loewner matrix
Linear Algebra and its Applications, 1993 This paper studies the so-called compatibility of a polynomial of degree \(n\) and a symmetric \(n \times n\) matrix. Similar to the compatibility of a Hankel matrix and a polynomial the authors investigate the compatibility of a polynomial and a symmetric Loewner matrix.
Zdeněk Vavřín, Miroslav Fiedler
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A complex associated with a symmetric matrix [PDF]
Kyoto Journal of Mathematics, 1977 Goto, Shiro, Tachibana, Sadao
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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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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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