ApplyLinearTransformPlot - Maple Help

Student[LinearAlgebra]

 ApplyLinearTransformPlot
 apply a linear transformation to a plot

 Calling Sequence ApplyLinearTransformPlot(M2, P2, opts) ApplyLinearTransformPlot(M3, P3, opts)

Parameters

 M2 - 2x2 Matrix M3 - 3x3 Matrix P2 - 2-D plot, list of 2-D points, or one of circle, grid, or square P3 - 3-D plot, list of 3-D points, or one of sphere, grid, or cube opts - 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

Description

 • 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 $x\to \mathrm{signum}\left(x\right)\mathrm{ln}\left(|x|+1\right)$ 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $\mathrm{infolevel}\left[\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right]≔1:$
 > $\mathrm{M1}≔⟨⟨1,\frac{1}{3}⟩|⟨\frac{1}{2},-\frac{1}{2}⟩⟩:$
 > $\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M1},\mathrm{output}=\mathrm{animation}\right)$
 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. >
 > $\mathrm{M2}≔⟨⟨1.0,0.2⟩|⟨0.3,0.9⟩⟩:$
 > $\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M2},\mathrm{iterations}=10,\mathrm{output}=\mathrm{animation}\right)$
 Determinant: .84 Norm:        1.206 Eigenvalue: 1.200 Multiplicity: 1 Eigenvector: < .8321, .5547 > Eigenvalue: .7000 Multiplicity: 1 Eigenvector: < -.7071, .7071 >
 > $\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M2},\mathrm{iterations}=10,\mathrm{output}=\mathrm{animation},\mathrm{trace}=4\right)$
 Determinant: .84 Norm:        1.206 Eigenvalue: 1.200 Multiplicity: 1 Eigenvector: < .8321, .5547 > Eigenvalue: .7000 Multiplicity: 1 Eigenvector: < -.7071, .7071 >
 > $\mathrm{M3}≔⟨⟨1.,0.2,0.3⟩|⟨0.3,0.9,0.3⟩|⟨0.2,0.2,1.⟩⟩:$
 > $\mathrm{ApplyLinearTransformPlot}\left(\mathrm{M3},\mathrm{grid},\mathrm{output}=\mathrm{animation}\right)$
 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, .2776e-15 >