A generalized inverse for matrices

1 July 1955

journal article
research article
Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society

Vol. 51 (3) , 406-413
https://doi.org/10.1017/s0305004100030401

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.

Keywords

This publication has 4 references indexed in Scilit:

Rectangular reciprocal matrices, with special reference to geodetic calculations
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ON DIAGONABLE AND NORMAL MATRICES
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Published by American Mathematical Society (AMS) ,1934