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必赢242net2024年学术报告系列讲座(十)

发布于:2024-01-25 浏览:

告题目The Generation of All Regular Rational Orthogonal Matrices

主讲人张浩助理教授

2024年1月27日(周六)上午10:55

:基础楼317学习室

主办单位:必赢242net

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.

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