分块矩阵Drazin逆的简单结果  

Simple Results for Drazin Inverse of Block Matrix

作　　者：杨晓英[1] 王亚强 刘新[1] YANG Xiao-ying;WANG Ya-qiang;LIU Xin(Department of Basic Education,Sichuan Information Technology College,Guangyuan Sichuan 628017,China;School of Mathematics and Information Sciences,Baoji University of Arts and Sciences,Baoji Shaanxi 721013,China)

机构地区：[1]四川信息职业技术学院人文学院,四川广元628017 [2]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《西华师范大学学报（自然科学版）》2022年第4期405-408,419,共5页Journal of China West Normal University(Natural Sciences)

基　　金：陕西省自然科学基金项目(2020JM-622);四川信息职业技术学院数学应用研究中心资助项目(2021KC01)。

摘　　要：分块矩阵的Drazin逆在信息安全、图像增强以及神经网络中有着广泛的应用。本文根据分块矩阵拆分为简单矩阵的思想,先将原矩阵进行矩阵分裂,应用Drazin逆的性质,得出分块矩阵Drazin逆需满足的部分条件,再将矩阵进行二次分裂,然后应用引理,得出矩阵Drazin逆需满足的其余条件,进而得出分块矩阵Drazin逆在一定条件下新的表达式。文中所给条件更为简单,结论也更具有一般性。Drazin inverse of block matrix has a wide range of applications in information security,image enhancement and neural networks.Firstly,in accordance with the thought of splitting block matrices into simple matrices,this paper splits the original matrix into two simple matrices and apply the properties of Drazin inverse to get some conditions needed for Drazin inverse of the block matrix.Then,the matrix is split twice and the rest of the conditions that need to be satisfied are obtained by the aid of lemma.After that,the new expression for Drazin inverse of the block matrix under certain conditions is obtained.The conditions given in the paper are simpler and the conclusions are more general.

关 键 词：分块矩阵 DRAZIN逆 幂零矩阵 矩阵分裂 指数 

分 类 号：O151.21[理学—数学]