Matrix Eigenvalues (WMA link)
Eigenvectors
Eigenvectors[{{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}]
Eigenvectors[{{1, 0, 0}, {0, 1, 0}, {0, 0, 0}}]
Eigenvectors[{{2, 0, 0}, {0, -1, 0}, {0, 0, 0}}]
Eigenvectors[{{0.1, 0.2}, {0.8, 0.5}}]