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General determinantal representation of pseudoinverses and its computation. (English) Zbl 0866.65031
Summary: We establish a general determinantal representation of generalized inverses and a general form of different definitions of rectangular determinants and induced generated inverses, in terms of minors of a matrix, satisfying certain conditions. Using this representation we obtain a general algorithm for the exact computation of different classes of pseudoinverses: Moore-Penrose inverse, 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.

##### MSC:
 65F20 Numerical solutions to overdetermined systems, pseudoinverses