A generalization of Moore-Penrose biorthogonal systems
Masaya Matsuura · Electronic Journal of Linear Algebra · 2003
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.