The ApplyLinearTransformPlot(M) command plots a circle or sphere and 4 (default value) successive images of that object under the given transformation.

The ApplyLinearTransformPlot(M,P) command plots the object P and 4 (default value) successive images of that object under the transformation defined by M.  P can be a plot object, a list of points, or one of the keywords circle, cube, grid, sphere, or square.  A list of points can be represented as a list of lists of two algebraic values in the 2-D case, and a list of lists of three algebraic values in the 3-D case.

The opts argument can include any of the Student plot options or any of the following equations that set plot options.

iterations = posint

The number of times the given linear transformation is applied to the object. By default, 4 iterations are applied.

logscale = true or false

If this option is set to true, the transformation $x\to \mathrm{signum}\left(x\right)\ln \left(\|x\|\+1\right)$ is applied to each point. [Default: false]

output = plot or animation

This option controls the return value of the function. [Default: plot]

* output = plot specifies a plot, showing P and its image under M applied as often as specified by the iterations option.

* output = animation specifies an animation, where the first iteration shows P, with subsequent frames showing the transformation M applied successively.

style = point or line

Selects whether to plot a list of points as points or connected by line segments.  This option is ignored if P is not a list of points. [Default: point]

trace = nonnegint or infinity

During an animation, up to this many previous frames will be displayed in the current one.  [Default: $0$]

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

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

$\mathrm{infolevel}\left[\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right]≔1\:$

$\mathrm{M1}≔⟨⟨1\,\frac{1}{3}⟩|⟨\frac{1}{2}\,-\frac{1}{2}⟩⟩\:$

$\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M1}\,\mathrm{output}=\mathrm{animation}\right)$

Determinant: -2/3
Norm:        (29/36+1/36*265^(1/2))^(1/2)

Eigenvalue: 1/4+1/12*105^(1/2)
Multiplicity: 1
Eigenvector: < 4.803, 1. >

Eigenvalue: 1/4-1/12*105^(1/2)
Multiplicity: 1
Eigenvector: < -.3117, 1. >

$\mathrm{M2}≔⟨⟨1.0\&comma;0.2⟩|⟨0.3\&comma;0.9⟩⟩\&colon;$

$\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M2}\&comma;\mathrm{iterations}=10\&comma;\mathrm{output}=\mathrm{animation}\right)$

Determinant: .84
Norm:        1.206

Eigenvalue: 1.200
Multiplicity: 1
Eigenvector: < .8321, .5547 >

Eigenvalue: .7000
Multiplicity: 1
Eigenvector: < -.7071, .7071 >

$\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M2}\&comma;\mathrm{iterations}=10\&comma;\mathrm{output}=\mathrm{animation}\&comma;\mathrm{trace}=4\right)$

Determinant: .84
Norm:        1.206

Eigenvalue: 1.200
Multiplicity: 1
Eigenvector: < .8321, .5547 >

Eigenvalue: .7000
Multiplicity: 1
Eigenvector: < -.7071, .7071 >

$\mathrm{M3}≔⟨⟨1.\&comma;0.2\&comma;0.3⟩\left|⟨0.3\&comma;0.9\&comma;0.3⟩\right|⟨0.2\&comma;0.2\&comma;1.⟩⟩\&colon;$

$\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M3}\&comma;\mathrm{grid}\&comma;\mathrm{output}=\mathrm{animation}\right)$

Determinant: .756
Norm:        1.473

Eigenvalue: .7394
Multiplicity: 1
Eigenvector: < -.7874, .3419, .5129 >

Eigenvalue: 1.461
Multiplicity: 1
Eigenvector: < .5857, .4496, .6744 >

Eigenvalue: .7000
Multiplicity: 1
Eigenvector: < .7071, -.7071, .3955e-15 >