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arXiv · 1707.00055

Drazin inverses of the sum of four matrices and its applications

Daochang Zhang·Dijana Mosi\' c·Li Guo
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Abstract

Our aim is to establish relations between Drazin inverses of the pesudo-block matrix $(P,Q,R,S)$ and the block matrix composed of $P,R,S,Q$, where $R^2=S^2=0$. Based on the relations, we give representations for Drazin inverses of the sum $P+Q+R+S$ under weaker restrictions. As its applications, several expressions for Drazin inverses of a $2\times 2$ block matrix are presented under some assumptions. Our results generalize several results in the literature.

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Daochang Zhang, Dijana Mosi\' c, Li Guo. 2017-06-30. Drazin inverses of the sum of four matrices and its applications. https://arxiv.org/abs/1707.00055

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