JordanDecomposition

JordanDecomposition[m] yields the Jordan decomposition of a square matrix m as a list {s, j} where s is a similarity matrix and j is the Jordan canonical form.

Examples

Jordan decomposition:

{s, j} = JordanDecomposition[{{5, 4, 2, 1}, {0, 1, -1, -1}, {-1, -1, 3, 0}, {1, 1, -1, 2}}]

Simple case:

JordanDecomposition[{{2, 1}, {0, 2}}]
(* {{{1, 0}, {0, 1}}, {{2, 1}, {0, 2}}} *)

Please visit the official Wolfram Language Reference for more details.