EigenvaluesTutor - Maple Help
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Student[LinearAlgebra][EigenvaluesTutor] - interactive and step-by-step matrix eigenvalues

Calling Sequence

EigenvaluesTutor(M, opts)

Parameters

M

-

square Matrix

opts

-

(optional) equation(s) of the form option=value where equation is output or displaystyle

Description

• 

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

• 

The EigenvaluesTutor(M) command presents the techniques used in finding the eigenvalues of the square matrix  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.

• 

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

(1)

(2)

See Also

factor, Student[LinearAlgebra], Student[LinearAlgebra][Determinant], Student[LinearAlgebra][Eigenvalues], Student[LinearAlgebra][EigenvectorsTutor]


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