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

Finding the eigenvalues

Solving the equation $-t_i\mathrm{Id}+M=0$ for each eigenvalue $t_i$

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 EigenvectorsTutor(M) command returns the eigenvectors as a set of column Vectors.

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

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

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

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