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A generalized inverse for matrices

Published online by Cambridge University Press:  24 October 2008

R. Penrose
R. Penrose
Affiliation:
St John's CollegeCambridge
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This paper describes a generalization of the inverse of a non-singular matrix, as the unique solution of a certain set of equations. This generalized inverse exists for any (possibly rectangular) matrix whatsoever with complex elements. It is used here for solving linear matrix equations, and among other applications for finding an expression for the principal idempotent elements of a matrix. Also a new type of spectral decomposition is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 3 , July 1955 , pp. 406 - 413
Copyright
Copyright © Cambridge Philosophical Society 1955

References

REFERENCES

(1)Autonne, L.Sur les matrices hypohermitiennes et sur les matrices unitaires. Ann. Univ. Lyon, (2), 38 (1915), 1–77.Google Scholar
(2)Bjerhammar, A.Rectangular reciprocal matrices, with special reference to geodetic calculations. Bull. géod. int. (1951), pp. 188–220.CrossRefGoogle Scholar
(3)Cecioni, F.Sopra operazioni algebriche. Ann. Scu. norm. sup. Pisa, 11 (1910), 17–20.Google Scholar
(4)Drazin, M. P.On diagonable and normal matrices. Quart. J. Math. (2), 2 (1951), 189–98.Google Scholar
(5)Halmos, P. R.Finite dimensional vector spaces (Princeton, 1942).Google Scholar
(6)Murray, F. J. and von Neumann, J.On rings of operators. Ann. Math., Princeton, (2), 37 (1936), 141–3.CrossRefGoogle Scholar
(7)Wedderburn, J. H. M.Lectures on matrices (Colloq. Publ. Amer. math. Soc. no. 17, 1934).CrossRefGoogle Scholar