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 member 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 the closed-form formula of the inverse of the considered matrix.