Journal ArticleDOI
An alternative to the Brauer set
TLDR
In this paper, an inclusion region for the eigenvalues of a matrix that can be considered an alternative to the Brauer set is derived, accompanied by non-singularity conditions.Abstract:
We derive an inclusion region for the eigenvalues of a matrix that can be considered an alternative to the Brauer set. It is accompanied by non-singularity conditions.read more
Citations
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Journal ArticleDOI
A new eigenvalue inclusion set for tensors and its applications
Chaoqian Li,Zhen Chen,Yaotang Li +2 more
TL;DR: In this article, a tensor eigenvalue inclusion set for weakly irreducible tensors was given, which proved to be tighter than those in L.Q. Qi (2005) and C.T. Kong (2014).
Journal ArticleDOI
Generalizations of Gershgorin disks and polynomial zeros
TL;DR: In this article, the authors derived inclusion regions for the eigenvalues of a general complex matrix that are generalizations of Gershgorin disks, along with nonsingularity conditions.
Journal ArticleDOI
Upper and lower bounds for the Perron root of a nonnegative matrix
TL;DR: Upper and lower bounds for the Perron root of a nonnegative matrix are derived by using generalized Gershgorin inclusion regions by using universal inclusion regions for sparse matrices.
Posted Content
Exclusion sets for eigenvalues of matrices
Suhua Li,Chaoqian Li,Yaotang Li +2 more
TL;DR: In this paper, the Brauer-type eigenvalue inclusion sets are used to locate all eigenvalues of a matrix more precisely, including some sets which do not include any eigen value of the matrix from the well-known Brauer set.
Journal ArticleDOI
A new localization set for generalized eigenvalues
Jing Gao,Chaoqian Li +1 more
TL;DR: A new localization set for generalized eigenvalues is obtained and it is shown that the new set is tighter than that in (Numer. Linear Algebra Appl. 16:883-898, 2009).
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Book
Geršgorin and his circles
TL;DR: In this paper, Taussky-Todd et al. studied the original results, and their extensions, of the Russian mathematician, SA Gersgorin, who wrote a seminal paper in 1931, on how to easily obtain estimates of all n eigenvalues (characteristic values) of any given n-by-n complex matrix.
Journal ArticleDOI
Matrices eigenvalues, and directed graphs
TL;DR: In this paper, the authors show how several classical results concerning inclusion regions and estimates for the eigenvalues of matrices can be unified and generalized by the use of directed graphs.