%0 Journal Article 
%A Stanimirovic, Predrag S.
%A Ciric, Miroslav
%A Lastra Sedano, Alberto
%A Sendra Pons, Juan Rafael
%A Sendra Pons, Juana
%T Representations and geometrical properties of generalized inverses over fields
%D 2021
%@ 0308-1087
%U http://hdl.handle.net/10017/50372
%X In this paper, as a generalization of Urquhart’s formulas, we present a full description of the sets
of inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vector
space with an affine space, we analyze geometrical properties of the main generalized inverse sets. We
prove that the set of inner inverses, and the set of (B, C)-inverses, form affine subspaces and we study
their dimensions. Furthermore, under some hypotheses, we prove that the set of outer inverses is not
an affine subspace but it is an affine algebraic variety. We also provide lower and upper bounds for the
dimension of the outer inverse set.
%K Outer inverses
%K Inner inverses
%K Moore-Penrose inverse
%K (B, C) inverse
%K Affine subspaces
%K Urquhart's formula
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala