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.
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Completion problems of partial $ N_0^1 $-matrices under directed 2-trees
AIMS MathematicsA matrix completion problem asks whether a partial matrix has a completion to a conventional matrix with a desired property. C. Mendes Ara$ \acute {u} $jo and J. R.
Gu-Fang Mou
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The hidden symmetries in the PMNS matrix and the light sterile neutrino(s)
, 2015 The approximately symmetric form of the PMNS matrix suggests that there could exist a hidden symmetry which makes the PMNS matrix different from the CKM matrix for quarks. In literature, all the proposed fully symmetric textures exhibit an explicit $\mu-\
Chen, Shuai +4 more
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Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue
Special Matrices, 2020 Let A = [aij] be a real symmetric matrix. If f : (0, ∞) → [0, ∞) is a Bernstein function, a sufficient condition for the matrix [f (aij)] to have only one positive eigenvalue is presented.
Al-Saafin Doaa, Garloff Jürgen
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The derivative of an orthogonal matrix of eigenvectors of a symmetric matrix
Linear Algebra and its Applications, 1997 Let \(M\) be a real symmetric \(p\times p\) matrix with distinct eigenvalues \(\lambda_i\) and associated normalized eigenvectors \(w_i\), \(1\leq i\leq p\). There are real-valued functions \(\psi_i\) and vector-valued functions \(f_i\) defined for all matrices \(Z\) in some neighborhood \({\mathcal N} (M) \subseteq \mathbb{R}^{p \times p}\) of \(M ...
Kollo, T., Neudecker, H.
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PT symmetry and large-N models
, 2008 Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model.
Bender C M +4 more
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Stability Analysis and Stabilization of Linear Symmetric Matrix-Valued Continuous, Discrete, and Impulsive Dynamical Systems -- A Unified Approach for the Stability Analysis of Linear Systems [PDF]
, 2021 Corentin Briat
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Miniversal deformations of pairs of symmetric matrices under congruence
, 2016 For each pair of complex symmetric matrices $(A,B)$ we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices $(\widetilde{A},\widetilde{B})$, close to $(A,B)$ can be reduced by congruence ...
Dmytryshyn, Andrii
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ZjuMatrix: C++ vector and matrix class library for finite element method
SoftwareXFinite element analysis is an indispensable and valuable tool widely used in the field of science and technology. It involves a multitude of matrix operations, storage of large banded matrices, and calculation of large-scale algebraic equations and ...
Shicheng Zheng, Rongqiao Xu
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A Simple Proof of the Classification of Normal Toeplitz Matrices
, 2002 We give an easy proof to show that every complex normal Toeplitz matrix is classified as either of type I or of type II. Instead of difference equations on elements in the matrix used in past studies, polynomial equations with coefficients of elements ...
Arimoto, Akio
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