Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach

Released on by C. R. Rao
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  • Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach Book Detail

  • Author : C. R. Rao
  • Release Date : 1988
  • Publisher :
  • Genre :
  • Pages : 22
  • ISBN 13 :
  • File Size : 91,91 MB
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Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach by C. R. Rao PDF Summary

Book Description: 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. (jhd).

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Selected Papers of C.R. Rao

Selected Papers of C.R. Rao

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This Is The Fourth Volume Of Selected Papers Of C. R. Rao Consisting Of 39 Papers Published During 1975-1985. These Papers Represent The Development Of Some Of

Generalized Inverses

Generalized Inverses

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This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. A