DOI: 10.1017/s0305004100030401. A generalized inverse for matrices

10.1017/s0305004100030401

Crossref journal-article

Cambridge University Press (CUP)

Mathematical Proceedings of the Cambridge Philosophical Society (56)

Abstract

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.

Bibliography

Penrose, R. (1955). A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society, 51(3), 406â413.

Authors 1

R. Penrose (first)

References 7 Referenced 3,197

10.1007/BF02526278
{'volume-title': 'Finite dimensional vector spaces', 'year': '1942', 'author': 'Halmos', 'key': 'S0305004100030401_ref005'} / Finite dimensional vector spaces by Halmos (1942)
{'key': 'S0305004100030401_ref003', 'first-page': '17', 'article-title': 'Sopra operazioni algebriche', 'volume': '11', 'author': 'Cecioni', 'year': '1910', 'journal-title': 'Ann. Scu. norm. sup. Pisa'} / Ann. Scu. norm. sup. Pisa / Sopra operazioni algebriche by Cecioni (1910)
10.2307/1968693
10.1093/qmath/2.1.189
(7) Wedderburn J. H. M. Lectures on matrices (Colloq. Publ. Amer. math. Soc. no. 17, 1934). (10.1090/coll/017)
{'key': 'S0305004100030401_ref001', 'first-page': '1', 'article-title': 'Sur les matrices hypohermitiennes et sur les matrices unitaires', 'volume': '38', 'author': 'Autonne', 'year': '1915', 'journal-title': 'Ann. Univ. Lyon'} / Ann. Univ. Lyon / Sur les matrices hypohermitiennes et sur les matrices unitaires by Autonne (1915)

Dates

Type	When
Created	16 years, 9 months ago (Nov. 7, 2008, 10:49 a.m.)
Deposited	6 years, 2 months ago (June 7, 2019, 1:32 a.m.)
Indexed	3 hours, 34 minutes ago (Aug. 23, 2025, 9:58 p.m.)
Issued	70 years, 1 month ago (July 1, 1955)
Published	70 years, 1 month ago (July 1, 1955)
Published Online	16 years, 10 months ago (Oct. 24, 2008)
Published Print	70 years, 1 month ago (July 1, 1955)

Funders 0

None

BibTeX

@article{Penrose_1955, title={A generalized inverse for matrices}, volume={51}, ISSN={1469-8064}, url={http://dx.doi.org/10.1017/s0305004100030401}, DOI={10.1017/s0305004100030401}, number={3}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Penrose, R.}, year={1955}, month=jul, pages={406–413} }

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