ELA, Volume 10, pp. 146-154, June 2003, abstract.

A Generalization of Moore-Penrose Biorthogonal Systems

Masaya Matsuura

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 g-inverses 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.