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Generalized inverse of linear transformations: a geometric approach
Authors:C.Radhakrishna Rao  Haruo Yanai
Affiliation:University of Pittsburgh Pittsburgh, Pennsylvania 15260, USA;Chiba University Chiba, Japan
Abstract:A generalized inverse of a linear transformation A:
/></figure> → <figure class=/></figure>, where <figure class=/></figure> and <figure class=/></figure> are arbitrary finite dimensional vector spaces, is defined using only geometrical concepts of linear transformations. The inverse is uniquely defined in terms of specified subspaces <math><mtext>L</mtext></math> ? <figure class=/></figure>, <math><mtext>M</mtext></math> ? <figure class=/></figure> and a linear transformation <em>N</em> satisfying some conditions. Such an inverse is called the <math><mtext>LM</mtext></math><em>N</em>-inverse. A Moore-Penrose type inverse is obtained by choosing <em>N</em> = 0. Some optimization problems are considered by choosing <figure class=/></figure> and <figure class=/></figure> as inner product spaces. Our results extend without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces.</td> </tr> <tr> <td align=
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