Geodesic
A generalization of Moore-Penrose biorthogonal systems
The electronic journal of linear algebra, Tome 10 (2003), pp. 146-154.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, the notion of Moore-Penrose biorthogonal systems is generalized. In [Fiedler, Moore-Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137-143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore-Penrose inverses and, in particular, the details of transformations derived from reflexive ginverses are studied. Furthermore, the characterization theorem of Moore-Penrose inverses in [Fiedler and Markham, A characterization of the Moore-Penrose inverse, Lin. Alg. Appl. 179 (1993), pp. 129-133] is extended to any reflexive g-inverse.
Classification : 15A03, 15A09
Keywords: generalized inverses, Moore-Penrose inverses, biorthogonal systems 
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     title = {A generalization of {Moore-Penrose} biorthogonal systems},
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Matsuura, Masaya. A generalization of Moore-Penrose biorthogonal systems. The electronic journal of linear algebra, Tome 10 (2003), pp. 146-154. http://geodesic.mathdoc.fr/item/ELA_2003__10__a14/