Eigenvectors at Work

Populations, Fibonacci and PageRank

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A Markov chain settles into a steady state: an eigenvector with eigenvalue 1.
• Repeated multiplication is dominated by the largest eigenvalue.
• Fibonacci grows by the golden ratio $\varphi \approx 1.618$, the largest eigenvalue of its matrix.

Steps

1. Two towns
2. The steady state
3. Fibonacci in a matrix
4. The growth rate
5. Growing populations
6. PageRank