[georgieporgie]

This started out taking baby steps, then took a huge leap in complexity right here:

Since the Fibonacci numbers are defined by a linear recurrence, we can express the recurrence as a matrix, and it’s easy to verify that...

It's been way too long since my math minor for me to understand that.

[robinhouston]

Sorry.

I think it’s only the jargon that’s confusing you. As long as you can remember (or look up) the definition of matrix multiplication, then it genuinely is easy to verify.

  [ fib(n-1) fib(n)   ] x [0 1]
  [ fib(n)   fib(n+1) ]   [1 1]
  
  = [ fib(n)   fib(n-1)+fib(n) ]
    [ fib(n+1) fib(n)+fib(n+1) ]
  
  = [ fib(n)   fib(n+1) ]
    [ fib(n+1) fib(n+2) ]