Lesson 17 of 20 · about 16 min

Diagonalization and matrix powers

Multiplying by a matrix a hundred times sounds like a lot of work, unless you use its eigenvectors. In the eigenvector basis, every matrix is just a stretch along the axes, and a hundred stretches are one big stretch. You'll watch vectors swing toward the strongest eigenvector, and use this trick to get a formula for the Fibonacci numbers.