The Eigenvalues(A) command returns the eigenvalues of the square Matrix A, that is, the values t such that Determinant(A - t . Id(Dimension(A))) = 0.  The eigenvalues are returned in a (column) Vector.

Note that eigenvalues are in general complex numbers.

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

$A≔⟨⟨1\,3⟩|⟨3\,-2⟩⟩$

$A≔\left[\begin{array}{cc}1& 3\\ 3& \mathrm{-2}\end{array}\right]$

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

$\left[\begin{array}{c}-\frac{1}{2}+\frac{3\sqrt{5}}{2}\\ -\frac{1}{2}-\frac{3\sqrt{5}}{2}\end{array}\right]$

$B≔⟨⟨1\,4\,-2⟩\left|⟨-1\,0\,1⟩\right|⟨-1\,2\,1⟩⟩$

$B≔\left[\begin{array}{ccc}1& \mathrm{-1}& \mathrm{-1}\\ 4& 0& 2\\ \mathrm{-2}& 1& 1\end{array}\right]$

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

$\left[\begin{array}{c}2\\ \mathrm{I}\\ \mathrm{-I}\end{array}\right]$