The EigenvaluesTutor(M) command presents the techniques used in finding the eigenvalues of the square matrix $M$ by:

Creating the matrix M - lambda*Id where Id is an identity matrix with dimensions equal to that of M

Taking the determinant of M - lambda*Id

Finding the roots of the resulting characteristic polynomial

The Matrix M must be square and of dimension 4 at most.

Floating-point numbers in M are converted to rationals before computation begins.

If the symbolic expression representing an eigenvalue grows too large, then the value displayed in the Maplet application window is a floating-point approximation to it (obtained by applying evalf).  The underlying computations continue to be performed using exact arithmetic, however.

The EigenvaluesTutor(M) command returns the eigenvalues as a column Vector.

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

$M≔⟨⟨1\,2\,0⟩\|⟨2\,3\,2⟩\|⟨0\,2\,1⟩⟩$

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

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