A geometrical approach on generalized inverses by Neumann-type series

By Joan-Josep Climent, N. Thome, Yimin Wei. 2001

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The convergence of the Neumann-type series to {1,2}-inverses has been shown by K. Tanabe [Linear Algebra Appl. 10 (1975) 163]. In this paper, these results indicating conditions characterizing the convergence of this series to different generalized inverses are extended. In addition, these results for obtaining different generalized inverses from the hyperpower method are applied. Finally, generalized involutory matrices are introduced and characterized using the obtained results.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d90b1ef6495c900a1f86b91f753dad07bf1e7876