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Student[LinearAlgebra][ApplyLinearTransformPlot] - apply a linear transformation to a plot
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Calling Sequence
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ApplyLinearTransformPlot(M2, P2, opts)
ApplyLinearTransformPlot(M3, P3, opts)
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Parameters
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M2
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2x2 Matrix
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M3
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3x3 Matrix
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P2
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2-D plot, list of 2-D points, or one of circle, grid, or square
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P3
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-
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3-D plot, list of 3-D points, or one of sphere, grid, or cube
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opts
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plotting options or equation(s) of the form option = value where option is one of iterations, logscale, output, style, trace, or Student[plot options]; specify options for the plot
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Description
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The ApplyLinearTransformPlot(M) command plots a circle or sphere and 4 (default value) successive images of that object under the given transformation.
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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.
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The opts argument can include any of the Student plot options or any of the following equations that set plot options.
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The number of times the given linear transformation is applied to the object. By default, 4 iterations are applied.
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If this option is set to true, the transformation  is applied to each point. [Default: false]
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output = plot or animation
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This option controls the return value of the function. [Default: plot]
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* output = plot specifies a plot, showing P and its image under M applied as often as specified by the iterations option.
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* output = animation specifies an animation, where the first iteration shows P, with subsequent frames showing the transformation M applied successively.
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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]
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trace = nonnegint or infinity
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During an animation, up to this many previous frames will be displayed in the current one. [Default:  ]
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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.
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Examples
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![with(Student[LinearAlgebra])](/support/helpjp/helpview.aspx?si=4080/file04967/math246.png)
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![infolevel[Student[LinearAlgebra]] := 1](/support/helpjp/helpview.aspx?si=4080/file04967/math250.png)
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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. >
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Determinant: .84
Norm: 1.206
Eigenvalue: 1.200
Multiplicity: 1
Eigenvector: < .8321, .5547 >
Eigenvalue: .7000
Multiplicity: 1
Eigenvector: < -.7071, .7071 >
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Determinant: .84
Norm: 1.206
Eigenvalue: 1.200
Multiplicity: 1
Eigenvector: < .8321, .5547 >
Eigenvalue: .7000
Multiplicity: 1
Eigenvector: < -.7071, .7071 >
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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, .2613e-15 >
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