On the trace-zero doubly stochastic matrices of order 5

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-10-21 DOI:10.1016/j.laa.2024.10.020

Amrita Mandal , Bibhas Adhikari

引用次数: 0

Abstract

We propose a graph theoretic approach to determine the trace of the product of two permutation matrices through a weighted digraph representation for a pair of permutation matrices. Consequently, we derive trace-zero doubly stochastic (DS) matrices of order 5 whose k-th power is also a trace-zero DS matrix for

k \in {2, 3, 4, 5}

. Then, we determine necessary conditions for the coefficients of a generic polynomial of degree 5 to be realizable as the characteristic polynomial of a trace-zero DS matrix of order 5. Finally, we approximate the eigenvalue region of trace-zero DS matrices of order 5.

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关于阶数为 5 的痕零双随机矩阵

我们提出了一种图论方法，通过一对置换矩阵的加权数图表示来确定两个置换矩阵乘积的迹。因此，我们推导出了阶数为 5 的迹零双重随机（DS）矩阵，其 k 次幂也是 k∈{2,3,4,5} 的迹零 DS 矩阵。然后，我们确定了一般 5 阶多项式系数可变为 5 阶微量为零 DS 矩阵特征多项式的必要条件。最后，我们逼近了阶为 5 的痕零 DS 矩阵的特征值区域。

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.