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Generalization of the Moore–Penrose inverse

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In order to extend the notation of the Moore–Penrose inverse from an operator with closed range to a generalized Drazin invertible operator, we present a new generalized inverse which is called the generalized Moore–Penrose inverse. We consider a number of characterizations and different representations of the generalized Moore–Penrose inverse. Inspired by these representations, we establish maximal classes of operators for which the representations of the generalized Moore–Penrose inverse are still valid. Some canonical forms for the generalized Moore–Penrose inverse are proved. The dual generalized Moore–Penrose inverse is defined and investigated too. Applying the generalized Moore–Penrose and dual generalized Moore–Penrose inverses, we solve some systems of linear equations.

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Acknowledgements

The funding has been recevied from Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja with Grant No. 174007

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  1. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, Niš, 18000, Serbia

    Katarina S. Stojanović & Dijana Mosić

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  1. Katarina S. Stojanović
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  2. Dijana Mosić
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Correspondence to Dijana Mosić.

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The authors are supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174007.

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Stojanović, K.S., Mosić, D. Generalization of the Moore–Penrose inverse. RACSAM 114, 196 (2020). https://doi.org/10.1007/s13398-020-00928-x

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