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The Moore-Penrose inverse of a sum of matrices

Published online by Cambridge University Press:  09 April 2009

Ching-Hsiang Hung  and
Thomas L. Markham
Ching-Hsiang Hung
Affiliation:
Department of Mathematics, Claflin College, Orangeburg, South Carolina, Columbia, S.C. 29208, U.S.A.
Thomas L. Markham
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, S.C. 29208, U.S.A.
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Abstract

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Suppose U and V are to m × n matrices over the complex field. We obtain a representation for the Moore–Penrose inverse of the sum U + V. A well-known result of Cline is then derived as a special case of a corollary of this representation.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 4 , December 1977 , pp. 385 - 392
Copyright
Copyright © Australian Mathematical Society 1977

References

Cline, R. E. (1965), ‘Representation of the generalized inverse of sums of matrices’, SIAM J. Numer. Anal., Ser. B, 2, 99–114.Google Scholar
Hung, C. H. and Markham, T. L. (1975), ‘The Moore–Penrose Inverse of a partitioned matrix M = ()’, Linear Alg. and Appl. 11, 73–86.CrossRefGoogle Scholar
Pye, W. C., Boullion, T. L., and Atchison, T. A. (1973), ‘The Pseudo-inverse of a Centrosymmetric Matrix’, Linear Alg. and Appl. 6, 201–204.CrossRefGoogle Scholar