A Characterization of Subclasses of Generalized Inverses of Specified Rank

A Characterization of Subclasses of Generalized Inverses of Specified Rank

Rao and Mitra (1971) and Mitra (1972) characterized the class of generalized inverses having a specified rank of a matrix. The object of the present note is to characterize the class of all least squares g-inverses having a specified rank of a matrix. We also obtain the class of all least squares so...

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Veröffentlicht in:Sankhya. Series A 1974-04, Vol.36 (2), p.214-218
1. Verfasser: Bhimasankaram, P.
Format: Artikel
Sprache:eng
Schlagworte:
Integers
Least squares
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Zusammenfassung:Rao and Mitra (1971) and Mitra (1972) characterized the class of generalized inverses having a specified rank of a matrix. The object of the present note is to characterize the class of all least squares g-inverses having a specified rank of a matrix. We also obtain the class of all least squares solutions to an inconsistent equation AXB = C. We obtain necessary and sufficient conditions under which every least squares g-inverse of A+D is also a least squares g-inverse of A. Similar problem for all g-inverses was solved by Mitra (1972).
ISSN:0581-572X