Eigenvalue Power Iteration

Animated convergence of dominant eigenvector — power method and convergence rate
Matrix A (2×2)
Iteration: 0
λ estimate:
True λ₁:
|error|:
Ratio λ₂/λ₁:
Power iteration: vₙ = Avₙ₋₁ / ‖Avₙ₋₁‖. Converges to dominant eigenvector with rate |λ₂/λ₁|ⁿ.

Rayleigh quotient: λ ≈ vᵀAv / vᵀv — best eigenvalue estimate from eigenvector.

Convergence: geometric with ratio r = |λ₂/λ₁| — faster when eigenvalues are well-separated.

Circle: shows unit circle with current vector (cyan) converging to true eigenvector (green).

Bottom: convergence of |λ estimate − λ true| — log scale shows linear convergence (geometric rate).