One second to compute the largest Fibonacci number I can

Most of us are familiar with the Fibonacci sequence. What's the largest Fibonacci number you can compute in 1 second? I'm not setting any world records, here; I don't own a supercomputer. You can criticise my code here: Addenda: __________ At 7:59, the e_{01}s in the bottom row are incorrect... [in my defense, the Fibonacci transition matrix is symmetric]. Thanks @andykhang404. Timestamps: __________ 00:00 - Introduction 01:06 - Recursion 02:35 - Memoisation 03:39 - “Linear“ nonrecursive algorithm 04:31 - Matrix-based algorithm 05:57 - Things add up 08:20 - Fast exponentiation algorithm 10:07 - Grade-school multiplication 11:45 - Multiplication through division 14:38 - Discreet improvements 17:27 - Fast and Furious (wysi) 19:36 - Golden medallist 22:10 - Thx 4 watching 22:38 - The ugly truth