Results 31 to 40 of about 2,374 (146)
Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices
Special Matrices, 2022 In this article, we determine upper and lower bounds for the spectral radius of nonnegative matrices. Introducing the notion of average 4-row sum of a nonnegative matrix, we extend various existing formulas for spectral radius bounds.
Adam Maria, Aretaki Aikaterini
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Perturbed spectra of defective matrices
Journal of Applied Mathematics, Volume 2003, Issue 3, Page 115-140, 2003., 2003 This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A + tE, where E ≠ 0 and t > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrix E varies over the sphere ‖E‖ = ρ > 0.
Mihail Konstantinov +2 more
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On real or integral skew Laplacian spectrum of digraphs
, 2020 For a simple connected graph G with n vertices and m edges, let −→ G be a digraph obtained by giving an arbitrary direction to the edges of G . In this paper, we consider the skew Laplacian matrix of a digraph −→ G and we obtain the skew Laplacian ...
S. Pirzada +2 more
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A convergence analysis of SOR iterative methods for linear systems with weak H-matrices
Open Mathematics, 2016 It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices).
Zhang Cheng-yi +2 more
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Journal of Applied Mathematics, Volume 2003, Issue 9, Page 459-485, 2003., 2003 A comprehensive treatment of Rayleigh‐Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore‐Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature.
Brian J. McCartin
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A lower bound for the smallest singular value
, 2012 In this paper, we obtain a lower bound for the smallest singular value of nonsingular matrices which is better than the bound presented by Yu and Gu [Linear Algebra Appl. 252(1997)25-38].
L. Zou
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, 2020 An inequality for matrices that interpolates between the Cauchy-Schwarz and the arithmetic-geometric mean inequalities for unitarily invariant norms has been obtained by Audenaert. Alakhrass obtained a related result to Audenaert’s inequality using a log-
M. Al-khlyleh, Fadi Alrimawi
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Bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math.
He Jun +4 more
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The nonexistence of rank 4 IP tensors in signature (1, 3)
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 5, Page 259-269, 2002., 2002 Let V be a real vector space of dimension 4 with a nondegenerate symmetric bilinear form of signature (1, 3). We show that there exists no algebraic curvature tensor R on V so that its associated skew‐symmetric operator R(⋅) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2‐planes in V.
Kelly Jeanne Pearson, Tan Zhang
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Two new eigenvalue localization sets for tensors and theirs applications
Open Mathematics, 2017 A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50).
Zhao Jianxing, Sang Caili
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