分块矩阵Drazin逆的简单结果

Simple Results for Drazin Inverse of Block Matrix

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.