Fibonacci Determinants

sequence

Fibonacci

Lucas

matrix size n

20

det

1	i	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
i	1	i	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	i	1	i	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	i	1	i	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	i	1	i	0	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	i	1	i	0	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	i	1	i	0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	i	1	i	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	i	1	i	0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	i	1	i	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	i	1	i	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	i	1	i	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	i	1	i	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	i	1	i	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	i	1	i	0	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	i	1	i	0	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	i	1	i	0	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	i	1	i	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	i	1	i
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	i	1

= 10946

The Fibonacci sequence of numbers appears in many surprising places. This Demonstration shows that you can obtain it by finding the determinant of a complex

n×n

tridiagonal matrix. By changing just a single matrix element you can obtain the Lucas numbers instead.