Topic
Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
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TL;DR: In this article, the Bauer-Fike technique was applied to the eigenvalue problem for regular periodic matrix pairs and condition numbers were obtained for individual as well as clusters of eigenvalues.
6 citations
TL;DR: In this paper, an envelope-type region ǫ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A is introduced and studied.
Abstract: We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.
6 citations
TL;DR: In this paper, the existence of an infinite number of eigenvalues for a model "three-particle" Schrodinger operator H was studied and the necessary and sufficient conditions for its existence below the lower boundary of its essential spectrum were proved.
Abstract: We study the existence of an infinite number of eigenvalues for a model “three-particle” Schrodinger operator H. We prove a theorem on the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of the model operator H below the lower boundary of its essential spectrum.
6 citations
TL;DR: In this article, the number of equations is equal to the multiplicity of the corresponding eigenvalues of an unperturbed discrete semibounded operator, where the number is the sum of all the equations in the system.
Abstract: To compute the eigenvalues of a perturbed discrete semibounded operator, systems are obtained for the first time in which the number of equations is equal to the multiplicity of the corresponding eigenvalues of the unperturbed operator.
6 citations
TL;DR: In this article, it was shown that block random matrices consisting of Wigner-type blocks have as many large (structural) eigenvalues as diagonal blocks, and the asymptotics of the eigen values is sharpened.
6 citations