Eigenvalues and eigenvectors
Given a function f that operates on a vector v
- f is a linear operator
- f(v) gives back a vector
- Possible outcomes of f are shrink/expand and rotate
Eigenvectors: Vectors that stay in the same direction under f
- These vectors are only shrunk or stretched by f
- They are basis vectors of f
Eigenvalue: How much the eigenvector is shrunk or stretched by f
- A scale factor associated with the eigenvector
- A number (may be complex)