Experiments / live

Eigenvectors playground

Most vectors get turned when a matrix hits them; a precious few only stretch. Set the four entries a, b, c, d of the matrix [[a, b], [c, d]] with the sliders below. A probe vector is swept around the unit circle (faint) and drawn next to its image Av; wherever the image lands back on the original line, that direction lights up — an eigen-direction. The readout shows the eigenvalues in closed form, and reports complex when the map is a pure rotation with no real eigenline. Then hit step to run one power-iteration step v ← Av/‖Av‖ and watch the arrow settle onto the dominant eigenvector. The full story is in the essay.