Glossary · Phase 2 · Math, when you need it
Eigenvector
A direction that a matrix only stretches or shrinks, without turning it.
The arrows that don't change direction (they only get longer, shorter, or flip around) are the matrix's eigenvectors. The amount each one is stretched by is its eigenvalue.
Try it now
Drag v onto a purple line and Av stays on it, stretched by λ. Off the lines, Av turns. Try Rotate 90°: no direction survives a quarter-turn, so there are no eigenvectors.
Learn it properly
Eigenvectors (intuition) · The directions a transformation leaves pointing the same way. About 25 minutes.
Never trained an AI?
Teach a small one to write, right in your browser. It takes about 20 seconds and needs no account.