Journal ArticleDOI
The Brauer-Ostrowski Theorem for Matrices of Operators
Gerd Herzog,Christoph Schmoeger +1 more
TLDR
The classical Brauer-Ostrowski Theorem gives a localization of the spectrum of a matrix by a union of Cassini ovals as mentioned in this paper, which is a result for operator matrices.Abstract:
The classical Brauer-Ostrowski Theorem gives a localization of the spectrum of a matrix by a union of Cassini ovals. In this paper we prove a corresponding result for operator matrices.read more
Citations
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Dissertation
Spectra of indefinite linear operator pencils
TL;DR: In this paper, a special class of non-self-adjoint linear pencils, called sign-indefinite linear pencil problems, are studied from the perspective of a two-parameter eigenvalue problem.
Journal ArticleDOI
A new Gershgorin-type result for the localisation of the spectrum of matrices
TL;DR: In this paper, a Gershgorin's type result on the localisation of the spectrum of a matrix is presented, which relies upon the method of Schur complements and outperforms the one based on the Cassini ovals of Ostrovski and Brauer.
Journal ArticleDOI
A new Gershgorin‐type result for the localisation of the spectrum of matrices
TL;DR: In this article, a Gershgorin's type result on the localisation of the spectrum of a matrix is presented, which relies upon the method of Schur complements, and yields estimates that hold without major differences in the cases of both scalar and operator matrices.
Journal ArticleDOI
The Ostrowski theorem for matrices of operators
Yaru Qi,Yuying Li,Yihui Kong +2 more
TL;DR: In this paper, the authors present the Ostrowski Theorem on the localization of the spectrum of an Riemannian matrix, which gives an estimate for the eigenvalues of a matrix by a union of some disks.
Journal ArticleDOI
The generalized Brauer–Ostrowski theorem for matrices of operators
Yaru Qi,Huanhuan Yang +1 more
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering 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.