A Lagrange matrices approach to confluent Cauchy matrices Original Research Article

We present a new approach to study inversion and factorization properties of confluent Cauchy matrices. We consider a class of generalized Vandermonde matrices, called Lagrange matrices, that are connected in a simple way with the Cauchy matrices. We apply the methods introduced in [Adv. Appl. Math. 10 (1989) 348] to obtain inversion and factorization theorems for Lagrange matrices and their confluent forms, and then derive corresponding results for Cauchy matrices.A Lagrange matrix V is associated with a pair of vectors (x0,x1,…,xn) and (y0,y1,…,yn). V is the matrix representation of the substitution operator that sends the vector image to the vector image, for any polynomial p of degree at most n.