Portal de Periódicos da CAPES

A generalized inverse for matrices

1955; Cambridge University Press; Volume: 51; Issue: 3 Linguagem: Inglês

10.1017/s0305004100030401

1469-8064

Roger Penrose,

Matrix Theory and Algorithms

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.