EigenvectorsTutor - Maple Help
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Student[LinearAlgebra][EigenvectorsTutor] - interactive and step-by-step matrix eigenvectors

 Calling Sequence EigenvectorsTutor(M, opts)

Parameters

 M - square Matrix opts - (optional) equation(s) of the form option=value where equation is output or displaystyle

Description

 • 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:
 1 Finding the eigenvalues
 2 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)

The output options are described in Student:-Basics:-OutputStepsRecord.  Use output = steps to get the default settings for displaying step-by-step solution output.

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

The displaystyle options are described in Student:-Basics:-OutputStepsRecord.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $M≔⟨⟨1,2,0⟩|⟨2,3,2⟩|⟨0,2,1⟩⟩$
 ${M}{≔}\left[\begin{array}{ccc}{1}& {2}& {0}\\ {2}& {3}& {2}\\ {0}& {2}& {1}\end{array}\right]$ (1)
 > $\mathrm{EigenvectorsTutor}\left(M\right)$
 > $\mathrm{EigenvectorsTutor}\left(M,\mathrm{output}=\mathrm{steps}\right)$