Determinants of some Hessenberg matrices with generating functions
A lower Hessenberg matrix \(A=(a_{ij})\) is an \(n \times n\) matrix whose entries above the superdiagonal are all zero but the matrix is not lower triangular, i.e., \(a_{ij} = 0\) for all \(j>i+1\). Similarly, \(A\) is an upper Hessenberg matrix when the transpose of \(A\) is a lower Hessenberg matrix. In this paper, the generating function method is used to determine some relationships between determinants of some special lower Hessenberg matrices whose entries are terms of certain sequences, and generating functions of these sequences. These relations generalize some previous known results. Also, these relations allow one to find the determinant of many lower Hessenberg matrices
scientific article; zbMATH DE number 7595340