首页   系科介绍   师资队伍   科研团队   本科生教学   研究生培养   招聘信息   联系我们

Previous Next
 
首页 >> 学术报告

A Matrix Decomposition and Its Applications

Fuzhen Zhang 教授(美国Nova Southeastern University)
2014年6月19日(周四)下午3点  数学楼126室
 
Abstract: We discuss a matrix decomposition, show the uniqueness and construction (of the $Z$ matrix in our main result) of the matrix decomposition, and give an affirmative answer to a question proposed in [J. Math. Anal. Appl. 407 (2013) 436-442]. The theorem is stated as Sectoral Decomposition:
Let $A$ be an $n\times n$ complex matrix such that its numerical range is contained in a sector in the 1st and 4th quadrants, i.e., $W(A)\subseteq S_{\alpha}$ for some $\alpha \in [0, \frac{\pi}{2})$. Then here exist an invertible matrix $X$ and a unitary diagonal matrix $Z={\rm diag} (e^{i\theta_1}, \dots, e^{i\theta_n})$ with all $|\theta_j|\leq \alpha$ such that $A=XZX^*$. Moreover, such a matrix $Z$ is unique up to permutation.
   
 
 
快捷链接 >>
 
系内资源 >>
 
教学园地 >>
 
  校外链接 >>    上海市核心数学与基础数学重点实验室    华师大-纽大联合数学中心    上海市数学会    中国数学会    美国数学会    欧洲数学会  
         
       Copyright 2012 All rights reserved    Department of Mathematics, East China Normal University    Tel: 86-21-54342609