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Zbl 0866.65031
Stanimirović, Predrag
General determinantal representation of pseudoinverses and its computation. (English)
[J] Rev. Acad. Ci. Exactas Fís. Quím. Nat. Zaragoza, II. Ser. 50, 41-49 (1995). ISSN 0370-3207

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 2000:: *65F20 Overdetermined systems (numerical linear algebra)

Keywords: determinantal representation; generalized inverses; algorithm; pseudoinverses; Moore-Penrose inverse; group inverse

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