Inverses and determinants of toeplitz-hessenberg matrices

Abstract

The inverses of Toeplitz-Hessenberg matrices are investigated. It is known that each inverse of such a matrix is a sum of a lower triangular matrix L and a matrix R of rank 1. The formulas of L and x, y such that xyT = R are derived. Using this result we propose an algorithm for inverting Toeplitz-Hessenberg matrices. Moreover, from the expression of the inverse a formula for the determinant is deduced.