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印度科学院院士Bapat教授学术报告

  发布日期:2016-05-09  浏览量:544


报告题目:  Squared distance matrix of a tree

:  Ravindra Bapat  (印度统计研究所教授,印度科学院院士)

报告时间:  20165 13(周五)下午15:00-16:00

报告地点: 磬苑校区澳门赌搏网站大全H306

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                                            201659

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 determiant  of , the inverse of , when it exists, and the inertia of .

报告人概况:  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, Springer 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, 2007-2011ISI Delhi中心主任。

 

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