Create the Fibonacci matrix as follows:

F = np.matrix([[1, 1], [1, 0]])
print("F", F)

The Fibonacci matrix appears as follows:

F [[1 1]
  [1 0]]

Calculate the 8th Fibonacci number (ignoring 0), by subtracting 1 from 8 and taking the power of the matrix. The Fibonacci number then appears on the diagonal:

print("8th Fibonacci", (F ** 7)[0, 0])

The Fibonacci number is as follows:

8th Fibonacci 21

The golden ratio formula, better known as Binet's formula, allows us to calculate Fibonacci numbers with a rounding step at the end. Calculate the first eight Fibonacci numbers:

n = np.arange(1, 9)
sqrt5 = np.sqrt(5)
phi = (1 + sqrt5)/2
fibonacci = np.rint((phi**n - (-1/phi)**n)/sqrt5)
print("Fibonacci", fibonacci)

The first eight Fibonacci numbers are as follows:

Fibonacci [  1.   1.   2.   3.   5.   8.  13.  21.]...