The EigenvectorsTutor(M) command by default opens a Maplet window which allows you to work interactively through solving for the eigenvectors of M. Options provide other ways to show the step-by-step solutions, as described below.

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.

The following options can be used to control how the problem is displayed and what output is returned, giving the ability to generate step-by-step solutions directly without going through the Maplet tutor interface:

output = steps,canvas,script,record,list,print,printf,typeset,link (default: maplet)

displaystyle= columns,compact,linear,brief (default: linear)

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

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

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

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

$\mathrm{EigenvectorsTutor}\left(M\,\mathrm{output}=\mathrm{steps}\right)$