Results 11 to 20 of about 3,570,033 (364)
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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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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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
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Self-Dual Codes, Symmetric Matrices, and Eigenvectors
IEEE Access, 2021 We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ using symmetric matrices and eigenvectors from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$ . Using this method, which is called a
Jon-Lark Kim, Whan-Hyuk Choi
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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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A Hebbian/Anti-Hebbian network for online sparse dictionary learning derived from symmetric matrix factorization [PDF]
Asilomar Conference on Signals, Systems and Computers, 2014 Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modelled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor ...
Tao Hu, Cengiz Pehlevan, D. Chklovskii
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On the spectrum of noisy blown-up matrices
Special Matrices, 2020 We study the eigenvalues of large perturbed matrices. We consider a pattern matrix P, we blow it up to get a large block-matrix Bn. We can observe only a noisy version of matrix Bn. So we add a random noise Wn to obtain the perturbed matrix An = Bn + Wn.
Fazekas István, Pecsora Sándor
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Two families of the simple iteration method, in comparison [PDF]
Компьютерные исследования и моделирование, 2012 Convergence to the solution of the linear system with real quadrate non singular matrix A with real necessary different sign eigen values of two families of simple iteration method: two-parametric and symmetrized one-parametric generated by these A and b
Pavel Nikolaevich Sorokin +1 more
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Decompositions of ideals of minors meeting a submatrix [PDF]
, 2015 We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix.
Neuerburg, Kent M., Teitler, Zach
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