Eigensystem

Eigensystem[m] gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m.

Eigensystem[{m, a}] gives the generalized eigenvalues and eigenvectors of m with respect to a.

Eigensystem[m, k] gives the eigenvalues and eigenvectors for the first k eigenvalues.

Examples

Eigenvalues and eigenvectors:

Eigensystem[{{1, 2}, {3, 4}}]
(* eigenvalues and corresponding eigenvectors *)

First k eigenvalues:

Eigensystem[HilbertMatrix[5], 2]

Please visit the official Wolfram Language Reference for more details.