RT info:eu-repo/semantics/article
T1 Representations and geometrical properties of generalized inverses over fields
A1 Stanimirovic, Predrag S.
A1 Ciric, Miroslav
A1 Lastra Sedano, Alberto
A1 Sendra Pons, Juan Rafael
A1 Sendra Pons, Juana
K1 Outer inverses
K1 Inner inverses
K1 Moore-Penrose inverse
K1 (B, C) inverse
K1 Affine subspaces
K1 Urquhart's formula
K1 Matemáticas
K1 Mathematics
AB In this paper, as a generalization of Urquhart’s formulas, we present a full description of the setsof inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vectorspace with an affine space, we analyze geometrical properties of the main generalized inverse sets. Weprove that the set of inner inverses, and the set of (B, C)-inverses, form affine subspaces and we studytheir dimensions. Furthermore, under some hypotheses, we prove that the set of outer inverses is notan affine subspace but it is an affine algebraic variety. We also provide lower and upper bounds for thedimension of the outer inverse set.
PB Taylor & Francis
SN 0308-1087
YR 2021
FD 2021-10-07
LK http://hdl.handle.net/10017/50372
UL http://hdl.handle.net/10017/50372
LA eng
NO Agencia Estatal de Investigación
DS MINDS@UW
RD 18-abr-2024