Generation of Fibonacci and Lucas Polynomials via Determinants

Generation of Fibonacci and Lucas Polynomials via Determinants

Alvin Sherman Library 2053

Number sequences such as the Fibonacci numbers or the Lucas numbers can be expressed using matrices and determinants. For example, the determinant of a n × nmatrix whose diagonal is made up of 1s and the super- and subdiagonals of i such that i2= -1, has been shown to give the (n + 1)th Fibonacci number. This paper will show how this representation can be extended so that the sequences generated by such determinants produce the Fibonacci and Lucas Polynomials.