Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1988
- Accession Number
- ADA197608
Entities
People
- Calyampudi Radhakrishna Rao
Organizations
- University of Pittsburgh