 interactive matrix eigenvectors - Maple Programming Help

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Student[LinearAlgebra][EigenvectorsTutor] - interactive matrix eigenvectors

 Calling Sequence EigenvectorsTutor(M)

Parameters

 M - square Matrix

Description

 • 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.

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