Results 1 to 10 of about 3,545,396 (319)
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, 2009 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 ...
Hassibi, Babak, Shadbakht, Sormeh
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Noncommutative symmetric functions with matrix parameters [PDF]
Journal of Algebraic Combinatorics, 2011 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
Lascoux, Alain +2 more
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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, 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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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.
Miroslav Fiedler, Zdeněk Vavřı́n
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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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Computing the inertias in symmetric matrix pencils
Linear Algebra and its Applications, 1994 Let \(S\) and \(T\) be \(n \times n\) real symmetric matrices and define \(P(S,T) = \{aS + bT : a,b \in \mathbb{R}\}\). A generalized pencil eigenvalue of the pencil \(P(S,T)\) is a pair \((a,b) \neq (0,0)\) such that \(aS + bT\) is singular. Suppose \(S\) is nonsingular and consider the open sectors of \(\mathbb{R}^ 2\) determined by the lines through
Frank Uhlig
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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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Generic symmetric matrix pencils with bounded rank [PDF]
Journal of Spectral Theory, 2018 We show that the set of $n \times n$ complex symmetric matrix pencils of rank at most $r$ is the union of the closures of $\lfloor r/2\rfloor +1$ sets of matrix pencils with some, explicitly described, complete eigenstructures.
Fernando De Ter'an +2 more
semanticscholar +1 more source