网站首页  学院概况  师资队伍  本科生教育  研究生教育  科学研究  党委专栏  学生活动 
当前位置: 网站首页 > 学术讲座 > 正文

New Rank Inequalities for the Hadamard Product with Applications

发布时间:2018年09月12日 17:16   浏览次数:
报告人 杨在 教授 年月 2018-09
17

题目:New Rank Inequalities for the Hadamard Product with Applications

报告人:杨在 教授(南京理工大学)

时间:2018.9.17(星期一)上午9:30-10:30

地点:数学学院东212

摘要:The Hadamard or elementwise product of matrices is fundamental in matrix analysis. Its study dates back to the early 20th century due to the mathematician Jacques Hadamard. The most well-known and also probably most important result is Schur product theorem, stating that the Hadamard product of positive (semi)definite matrices remains to be positive (semi)definite. In this talk, we will revisit the developments of Schur’s theorem in the past century. We provide two new rank inequalities for the Hadamard product, giving sufficient conditions under which the Hadamard product of positive semidefinite matrices is strictly positive definite. Applications of the new results are presented in matrix theory as well as in array processing to resolve a fundamental problem as to how many antennas are required to resolve a fixed number of sources. As a byproduct, we obtain a new rank inequality for the Khatri-Rao product of matrices which should be of independent interest.

关闭

Copyright © 2018四川大学数学学院版权所有
 地址:成都市一环路南一段24号
电话:028-85412720