On Matrices with Bidimensional Fibonacci Numbers

Abstract In this paper, the bidimensional extensions of the Fibonacci numbers are explored, along with a detailed examination of their properties, characteristics, and some identities. We introduce and study the matrices with bidimensional Fibonacci numbers, focusing in particular on their recurrence relation, key properties, determinant, and various other identities. It is our purpose to study the matrix version of bidimensional Fibonacci numbers and provide new results and sometimes extensions of some results existing in the literature. We aim to introduce these matrices using the bidimensional Fibonacci numbers and to give the determinant of these matrices.