The document defines eigenvalues and eigenvectors. An eigenvector is a non-zero vector whose direction does not change when a linear transformation is applied. The associated scalar multiplier is the eigenvalue. Eigenvalues are found by setting the determinant of A - λI equal to 0. This characteristic equation has roots that are the eigenvalues. Eigenvectors correspond to distinct eigenvalues and are nonzero solutions to (λI - A)x = 0. The document provides examples of finding eigenvalues and eigenvectors and lists several properties of eigenvalues and eigenvectors.