A note on the eigenvalue free intervals of some classes of signed threshold graphs

IF 1 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-01-01 DOI:10.1515/spma-2019-0014

M. Anđelić, T. Koledin, Z. Stanić

引用次数: 0

Abstract

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

查看原文本刊更多论文

关于一类有符号阈值图的特征值自由区间的注记

摘要我们考虑一类特殊的有符号阈值图及其特征值。如果Ġ是这样一个阈值图，并且Q（Ġ;）是由公平划分产生的商矩阵，则我们使用一系列初等矩阵运算来证明矩阵Q（ġ）–xI（x∈ℝ) 行等价于一个三对角矩阵，其行列式在某些条件下为常符号。通过这种方式，我们确定了Ġ没有特征值的某些区间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.