Power Iteration: Watching a Vector Converge to a Dominant Eigenvector (2D)

This 2D companion turns the abstract "eigenvectors are directions that don't rotate" statement into a discrete, watchable algorithm: a unit vector is repeatedly multiplied by the same 2×2 matrix A and renormalised, one step at a time, at a rate you control. A side panel exposes all four matrix entries, the starting angle and the step rate; live charts track the vector's angle and a Rayleigh-quotient estimate of the dominant eigenvalue converging toward the analytic value — or, when A's eigenvalues are complex, spinning forever instead, which the charts make just as visible as convergence.