LinearTransformPlot - Maple Help

Student[LinearAlgebra]

 LinearTransformPlot
 plot the action of a linear transformation

 Calling Sequence LinearTransformPlot(M, opts)

Parameters

 M - Matrix opts - plotting options or equation(s) of the form option=value where option is one of showeigenvectors, eigenoptions, shownullspace, nullspaceoptions, labeloptions, labels, normalize, spheregrid, subspace, subspaceoptions, or Student plot options; specify options for the plot

Description

 • The LinearTransformPlot(M) command, where M is an $mxn$ Matrix, plots the transformation of the interval [-1, 1], the unit circle, or the unit sphere for n = 1, 2, or 3, respectively, to the line, plane, or 3-space for m = 1, 2, or 3, respectively, under the action of M.
 • The opts argument can contain any of the Student plot options or any of the following equations that set plot options.
 showeigenvectors = true or false
 If M is a square matrix, this specifies whether its eigenvectors and their images are plotted.  If M is not square, this option is ignored. [Default: true]
 eigenoptions = list
 Provides options (for example, color and thickness) to the routine which plots the eigenvectors and their images.  This option is ignored if M is not square.
 shownullspace = true or false
 Specifies whether the null space of M is plotted. [Default: true]
 nullspaceoptions = list
 Provides options to the routine that plots the nullspace of M.
 labeloptions = list
 Provides options for the display of the labels, for example, font and color.
 labels = list({string,symbol}) or list(list({string,symbol}))
 Specifies the names to use as axis labels in the domain and range images. If given as list({string,symbol}) (for example, $\mathrm{labels}=\left["x","y","z"\right]$), the same labels are used for both the domain and range axes.  If given as a list of two list({string,symbol}), the first list of labels is used for the domain axes, and the second list is used for the range axes.  If fewer labels are provided than are required by the plot, missing labels are taken from the default values. [Default: [["x","y","z"],["x","y","z"]] ]
 normalize = true or false
 If set to true, the image object is scaled by the inverse of the norm of M, so that the domain object and image object have similar proportions.  [Default: true]
 spheregrid = posint
 Specifies the grid size used to plot the sphere.  A smaller value results in a more transparent sphere, but one which looks less spherical.  [Default: 16]
 subspace = Vector, list(Vector), or set(Vector)
 Specifies a subspace of the domain.  The subspace and its image of this subspace under the action of M are plotted.
 subspaceoptions = list
 Provides options to the routine that plots the subspace of the domain space, where the subspace is given in the subspace option.
 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

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $\mathrm{infolevel}\left[\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right]≔1:$

The commands to create the plots from the Plotting Guide are

 > $\mathrm{LinearTransformPlot}\left(⟨⟨-2,3,3⟩|⟨2,-3,2⟩|⟨3,2,-3⟩⟩\right)$
 Rank:  3 Norm:  5.573 Determinant:  65 Eigenvalue: -3/2+1/2*61^(1/2) Multiplicity: 1 Eigenvector: < 1.135, 1., 1. > Eigenvalue: -3/2-1/2*61^(1/2) Multiplicity: 1 Eigenvector: < -1.468, 1., 1. > Eigenvalue: -5 Multiplicity: 1 Eigenvector: < -2/3, 1, 0 >

Plot options not inside another option apply to the plot as a whole:

 > $\mathrm{LinearTransformPlot}\left(⟨⟨2,3⟩|⟨2,2⟩⟩,\mathrm{labels}=\left[\left["x","y"\right],\left["u","v"\right]\right],\mathrm{labeloptions}=\left[\mathrm{font}=\left[\mathrm{TIMES},\mathrm{ROMAN},12\right],\mathrm{color}=\mathrm{red}\right],\mathrm{captionfont}=\left[\mathrm{TIMES},\mathrm{ROMAN},20\right]\right)$
 Rank:  2 Norm:  4.562 Determinant:  -2 Eigenvalue: 2+6^(1/2) Multiplicity: 1 Eigenvector: < .8163, 1. > Eigenvalue: 2-6^(1/2) Multiplicity: 1 Eigenvector: < -.8163, 1. >

Other example:

 > $\mathrm{LinearTransformPlot}\left(⟨⟨2,0⟩|⟨0,4⟩|⟨2,3⟩⟩,\mathrm{normalize}=\mathrm{false}\right)$
 Rank:  2 Norm:  5.187