General determinantal representation of pseudoinverses. (English) Zbl 0948.15005

Stanimirović, P.

Mat. Vesn. 48, No. 1-2, 1-9 (1996).

This is a generalization of the paper by P. Stanimirović and M. Stanković [Mat. Vesn. 46, No. 1-2, 41-50 (1994; Zbl 0840.15005)] and various other results on representations of generalized inverses. It contains explicit formulae for elements of \(\{ i,j,k \}\)-inverse and group-inverse of a given matrix in terms of its subdeterminants. The formulae are proved by standard matrix algebra calculations.

Reviewer: Aleksandar Lipkovski (Beograd)

MSC:

15A09

Theory of matrix inversion and generalized inverses

Keywords:

generalized inverse; pseudoinverse; determinantal representation; group-inverse

Citations:

Zbl 0840.15005