Inclusion regions and bounds for the eigenvalues of matrices with a known eigenpair

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2020-01-01 DOI:10.1515/spma-2020-0115

Rachid Marsli, Frank J. Hall

引用次数: 1

Abstract

Abstract Let (λ, v) be a known real eigenpair of an n×n real matrix A. In this paper it is shown how to locate the other eigenvalues of A in terms of the components of v. The obtained region is a union of Gershgorin discs of the second type recently introduced by the authors in a previous paper. Two cases are considered depending on whether or not some of the components of v are equal to zero. Upper bounds are obtained, in two different ways, for the largest eigenvalue in absolute value of A other than. Detailed examples are provided. Although nonnegative irreducible matrices are somewhat emphasized, the main results in this paper are valid for any n × n real matrix with n≥3.

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具有已知本征对的矩阵的本征值的包含域和界

摘要设(λ， v)是一个已知的n×n实矩阵a的实特征对，本文给出了如何用v的分量来确定a的其他特征值，得到的区域是作者在上一篇文章中最近引入的第二类Gershgorin盘的并。考虑两种情况取决于v的某些分量是否等于零。用两种不同的方法得到了A的绝对值中最大特征值的上界，而不是。给出了详细的示例。虽然对非负不可约矩阵有一定的强调，但本文的主要结果对n≥3的任何n × n实矩阵都是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.