Eigen-everything

Eigenvectors, eigenvalues, eigenspaces! We will not stop with the "eigens"! Seriously though, eigen-everythings have many applications including finding "good" bases for a transformation (yes, "good" is a technical term in this context).

Introduction to eigenvalues and eigenvectors

Proof of formula for determining eigenvalues

Example solving for the eigenvalues of a 2x2 matrix

Finding eigenvectors and eigenspaces example

Eigenvalues of a 3x3 matrix

Eigenvectors and eigenspaces for a 3x3 matrix

Showing that an eigenbasis makes for good coordinate systems