Lesson 36 of 48
Eigenvalues and eigenvectors
The directions a transformation leaves alone.
Most vectors get turned by a matrix. A few only get stretched, and those few describe the transformation's character more compactly than the grid of numbers ever did.
Do this
Find the eigenvectors and eigenvalues of a 2×2 matrix by hand, then verify numerically that Av = λv for each. Then try a rotation matrix and see what happens.
The question that unlocks the next lesson
v is an eigenvector of A with eigenvalue λ. What does Av equal?
- A0
- Bλv — the same direction, scaled
- Cv + λ
- DA + λ