A simple proof of the Fisher–Fuller theorem

Abstract

Several years ago, Fisher and Fuller(1) proved that if P is a real square matrix with all members of its ‘nested set’ of principal minors non-zero, then there exists a real diagonal matrix, D, such that the characteristic roots of DP are all real, negative and distinct. This interesting and powerful result, used by the authors to derive further results concerning convergence of linear iterative processes, has since also proved of interest to economists studying the stability of economic general equilibrium.