Abstract
In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only if aa D(a+b) is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of (a + b)D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.
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Supported by the National Natural Science Foundation of China (11361009), the Guangxi Provincial Natural Science Foundation of China (2013GXNSFAA019008), and Science Research Project 2013 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities.
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Liu, Xj., Qin, Xl. & Julio, B. Some additive results on Drazin inverse. Appl. Math. J. Chin. Univ. 30, 479–490 (2015). https://doi.org/10.1007/s11766-015-3333-4
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DOI: https://doi.org/10.1007/s11766-015-3333-4