Representations for the Drazin inverses of block matrices

Li Guo,Wenming Du,Jie Wang,J.C.M Kao,W.-P Sung

doi:10.1051/matecconf/20166305037

Li Guo, Wenming Du + Show 3 more

Open Access

https://doi.org/10.1051/matecconf/20166305037

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Abstract

In this paper, we investigate representations of the Drazin inverse of a 2 × 2 block matrix. The Drazin inverse of a matrix is very important in various applied mathematical fields like machinery and automation, singular differential equations. We give a explicit representation of the Drazin inverse of a block matrix.

Highlights

In this paper, representations for the DrazinLet C nun denote the set of n u n complex inverse of 2 u 2 block matrix M, under the matrices
We introduce briefly an application of the Drazin inverse of a block matrix[2]
Wei,, Additive results for the generalized Drazin inverse, J

Summary

Introduction

Let C nun denote the set of n u n complex inverse of 2 u 2 block matrix M , under the matrices. BD 0ˈDS CB 0ˈDS CAB 0ˈDS CA2 0 ind ( A) , is called the index of A . The Drazin inverse is the unique matrix Ad C nun satisfying Lemma 1.1 [3]Let A C mun and B C num , ( AB)d A[(BA)2 ]d B .

Results

Conclusion