Some Properties of Hessenberg Matrices with Conditional Elements

Abstract

Hessenberg matrices are a class of structured matrices that play a fundamental role in various areas of mathematics and scientific computing. These matrices have diverse applications in numerical analysis, optimization, graph theory, and quantum mechanics, among others. This paper provides the determinants of the conditional Hessenberg matrices whose elements are the generalized bi-periodic Fibonacci numbers. Moreover, we find the inverse of some special type matrices which help us to find the determinant of the conditional Hessenberg matrices.