Abstract

Abstract : A generalized inverse of a linear transformation A: v yield w, where v and w are finite dimensional vector spaces, is defined using geometric concepts of linear transformations and projection operators. The inverse is uniquely defined in terms of specified subspaces m is a subset of v, 1 is a subset of w and a linear transformation N such that AN = O, NA = O. Such an inverse which is unique is called the 1mN-inverse. A Moore-Penrose type inverse is obtained by putting N=O. Applications to optimization problems when v and w are inner product spaces, such as least squares in a general setting, are discussed. The results given in the paper can be extended without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces. Keywords: G inverse; Linear transformation; Moore Penrose inverse; Projection operator.

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