A Generalization of Moore–penrose Biorthogonal Systems * Masaya Matsuura †
نویسنده
چکیده
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.
منابع مشابه
A generalization of Moore-Penrose biorthogonal systems
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 i...
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