The CharacteristicPolynomial(A, t) command returns the characteristic polynomial in t that has the eigenvalues of Matrix A as its roots (all multiplicities respected).

This polynomial is the determinant of $t\mathrm{Id}-A$, where Id is the identity Matrix with Dimension(A).

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$M≔⟨⟨1\,0\,0⟩\left|⟨1\,1\,0⟩\right|⟨0\,3\,2⟩⟩$

$M≔\left[\begin{array}{ccc}1& 1& 0\\ 0& 1& 3\\ 0& 0& 2\end{array}\right]$

$\mathrm{CharacteristicPolynomial}\left(M\,x\right)$

$x^3-4x^2+5x-2$

$\mathrm{solve}\left(\,x\right)$

$2,1,1$

$\mathrm{Eigenvalues}\left(M\right)$

$\left[\begin{array}{c}2\\ 1\\ 1\end{array}\right]$