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On best approximate solutions of linear matrix equations

Published online by Cambridge University Press:  24 October 2008

R. Penrose
R. Penrose
Affiliation:
St John's CollegeCambridge
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 17 - 19
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Bjerhammar, A.Rectangular reciprocal matrices with special reference to geodetic calculations. Bull. géod. int. (1951), pp. 188–220.Google Scholar
(2)Dwyer, P. S.Linear computations (New York, 1951), pp. 225–8.Google Scholar
(3)Moore, E. H.Bull. Amer. math. Soc. (2) 26 (1920), 394–5.Google Scholar
(4)Penrose, R.A generalized inverse for matrices. Proc. Camb. phil. Soc. 51 (1955), 406–13.Google Scholar
(5)Turnbull, H. W. and Aitken, A. C.Theory of canonical matrices (London, 1948), pp. 173–4.Google Scholar