Displaying similar documents to “New bounds for the minimum eigenvalue of 𝓜-tensors”

Two new eigenvalue localization sets for tensors and theirs applications

Jianxing Zhao, Caili Sang (2017)

Open Mathematics

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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). As an application, a weaker checkable sufficient condition for the positive (semi-)definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et...

Unified Spectral Bounds on the Chromatic Number

Clive Elphick, Pawel Wocjan (2015)

Discussiones Mathematicae Graph Theory

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One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenvalues of the adjacency, Laplacian and signless Laplacian matrices. The various known bounds...

Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

Jianxing Zhao, Caili Sang (2016)

Open Mathematics

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Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.