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On best approximate solutions of linear matrix equations

  • R. Penrose (a1)

In an earlier paper (4) it was shown how to define for any matrix a unique generalization of the inverse of a non-singular matrix. The purpose of the present note is to give a further application which has relevance to the statistical problem of finding ‘best’ approximate solutions of inconsistent systems of equations by the method of least squares. Some suggestions for computing this generalized inverse are also given.

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(1)Bjerhammar A.Rectangular reciprocal matrices with special reference to geodetic calculations. Bull. géod. int. (1951), pp. 188220.
(2)Dwyer P. S.Linear computations (New York, 1951), pp. 225–8.
(3)Moore E. H.Bull. Amer. math. Soc. (2) 26 (1920), 394–5.
(4)Penrose R.A generalized inverse for matrices. Proc. Camb. phil. Soc. 51 (1955), 406–13.
(5)Turnbull H. W. and Aitken A. C.Theory of canonical matrices (London, 1948), pp. 173–4.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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