CharacteristicPolynomial

CharacteristicPolynomial[m, x] gives the characteristic polynomial for the matrix m.

Examples

Characteristic polynomial:

CharacteristicPolynomial[{{1, 2}, {3, 4}}, x]
(* -5 - 5 x + x^2 *)

Roots give eigenvalues:

Solve[CharacteristicPolynomial[{{1, 2}, {3, 4}}, x] == 0, x]
(* {{x -> (5 - Sqrt[33])/2}, {x -> (5 + Sqrt[33])/2}} *)

Please visit the official Wolfram Language Reference for more details.