报告题目：The Generation of All Regular Rational Orthogonal Matrices

主讲人：张浩助理教授

时 间：2024年1月27日（周六）上午10：55

地 点：基础楼317学习室

主办单位：理学院

主讲人简介：

张浩，湖南大学数学学院助理教授。博士毕业于索邦大学。研究兴趣主要为解析数论、图论中的广义谱确定问题等。

摘要:

A rational orthogonal matrix Q is an orthogonal matrix with rational entries, and Q is called regular if each of its row sum is one, i.e., Qe = e with e the all-one vector. We give a method of generating all regular rational orthogonal matrices by using the classic Cayley transformation. At the heart of our method is a key new ingredient which is of independent interest, stating that given a square matrix M, then MP has -1 as an eigenvalue for every permutation matrix P if and only if either every row sum of M is −1 or every column sum of M is −1.