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 $xy^T = R$ 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.