On a property of Cauchy-like matrices

We introduce in this Note a property connecting the generators of a Cauchy-like matrix to the generators of its Schur complements. This property (formulas (6)) yields to a recursive process that can be used to devise a fast and direct inversion algorithm for Cauchy-like matrices (Section 4). The approach considered here is substantially simpler than those developed in some recent works on the subject ([2], [4], [6], [7], [8]).