报告题目: Squared distance matrix of a tree
报 告 人: RavindraBapat(印度统计研究所教授，印度科学院院士)
报告时间:2016年5 月13日(周五)下午15:00-16:00
报告地点: 磬苑校区数学科学学院H306
报告地点:安徽大学磬苑校区数学科学学院H306
主办单位：数学科学学院
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科学技术处
2016年5月10日
报告摘要：
Let be a connected graph with vertex set . The distance between vertices , is defined to be the minimum length (the number of edges) of a path from to . The distance matrix , or simply , is the matrix with -element equal to 0 if and if .According to a well-known result due to Graham and Pollak, if is a tree with vertices, then the determinant of the distance matrix of is . Thus the determinant depends only on the number of vertices I the tree and not on the tree itself.A formula for the inverse of the distance matrix of a tree was given by Graham and Lovász. Several generalizations of these two results have been proved. We first provide an overview of various distance matrices associated with a tree. These include a weighted analog of the classical distance matrix, a weighted analog with matrix weights, a -analog, and the exponential distance matrix, which has the -element equal to . We then consider the entry-wise square of the distance matrix of a tree. Thus the squared distance matrix has its -elemen equal to . In joint work with S. Sivasubramanian, we gave a formula for the determiantof , the inverse of , when it exists, and the inertia of .
报告人简介:
Ravindra Bapat 教授, 印度统计研究所教授，印度科学院院士。研究领域包括非负矩阵理论、矩阵不等式、图的矩阵以及广义逆等。已发表论文100余篇, 在Springer 和 Cambridge University Press 上出版专著多部, 2004年获得政府最佳文献奖, 2009年获J.C. Bose Fellowship。主要的社会服务工作包括: 2007-2008年任印度数学会理事长, 现担任权威期刊《Linear and Multilinear Algebra》、《 Electronic Journal of Linear Algebra》、《India Journal of Pure and Applied Mathematics》 和《Kerala Mathematical Association Bulletin》的编委, 现担任印度国家数学奥林匹克竞赛队总教练, 2007-2011任ISI Delhi中心主任。