Lesson 3.6MathCode~1 h

Special directions & PCA

Directions a matrix only stretches, and how they let you squash 100 dimensions into 2 you can see.

Module 3 · 0/7 done

Directions that don’t turn

You’ve seen that a matrix moves space around: it stretches, squashes, shears and rotates. Most arrows get pointed in a new direction. But many matrices have a few special directions that come out pointing exactly the same way, only longer or shorter.

Those are the eigenvectors (from German eigen, “own”: the matrix’s own directions). How much each one gets stretched is its eigenvalue, written $\lambda$ (“lambda”).

A\,\blue{\mathbf{v}} = \lambda\,\blue{\mathbf{v}}

ChallengeIn progress

Drag v until the matrix only stretches it: the orange arrow Av must line up with v.

Complete the challenge above to continue.