interactive matrix eigenvalues - Maple Programming Help

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Student[LinearAlgebra][EigenvaluesTutor] - interactive matrix eigenvalues

 Calling Sequence EigenvaluesTutor(M)

Parameters

 M - square Matrix

Description

 • The EigenvaluesTutor(M) command presents the techniques used in finding the eigenvalues of the square matrix $M$ by:
 1 Creating the matrix M - lambda*Id where Id is an identity matrix with dimensions equal to that of M
 2 Taking the determinant of M - lambda*Id
 3 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.

Examples

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