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Some additive results for the Drazin inverse and its application

Yang Xiaoying (Department of Basic Education, Sichuan Vocational College of Information Technology, Guangyuan, Sichuan, China)
Liu Xin (Department of Basic Education, Sichuan Vocational College of Information Technology, Guangyuan, Sichuan, China)
Chen Fubin (Department of Engineering, Oxbridge College, Kunming University of Science and Technology, Kunming, Yunnan, China)

In this paper, we give some formulas for the Drazin inverses of the sum of two matrices under conditions weaker than those used in some current literature. Also, we obtain representation for the Drazin inverse of a complex block matrix under some conditions.

Keywords: Drazin inverse, Block matrix, Matrix index, Generalized Schur complement