MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
General determinantal representation of pseudoinverses of matrices
Predrag Stanimirović

Abstract

In this paper we establish general determinantal representation of generalized inverses and general form of different definitions of rectangular determinants and induced general inverses, in terms of minors of a matrix, satisfying certain conditions. Using this representation we obtain a general algorithm for exact computation of different classes of pseudoinverses: Moore-Penrose and weighted Moore-Penrose inverse, group inverse, $\{1,2,3\}$, $\{1,2,4\}$, $\{1,2\}$ inverses, left/right inverses, Radić's and Stojaković's generalized inverses. We also give some examples which illustrate our results.

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Keywords: Pseudoinverse, determinantal representation, rectangular determinant, (weighted) Moore-Penrose inverse, group inverse

MSC: 15A09, 65F05

Pages:  1--9     

Volume  48 ,  Issue  1$-$2 ,  1996