A generalized inverse for matrices
Mathematical Proceedings of the Cambridge Philosophical SocietyPublished 1 July 1955Open access
Roger Penrose
Citations4,495
SJR quartileQ1
SJR score1.03
SNIP1.13
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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
Computer Science
The Quarterly Journal of MathematicsON DIAGONABLE AND NORMAL MATRICES
13 Citations1951Michael P. Drazin