On a special generalized Vandermonde matrix and its $LU$ factorization

Abstract

We consider a special class of the generalized Vandermonde matrices and obtain an $LU$ factorization for its members by giving closed-form formulae of the entries of $L$ and $U$. Moreover, we express the matrices $L$ and $U$ as products of 1-banded (bidiagonal) matrices. Our result is applied to give a closed-form formula for the inverse of the matrix considered.