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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>signumxln|x|+1 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

withStudent[LinearAlgebra]:

infolevel[Student[LinearAlgebra]]:=1:

M1:=1,13|12,12:

ApplyLinearTransformPlotM1,output=animation

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. >

M2:=1.0&comma;0.2&verbar;0.3&comma;0.9&colon;

ApplyLinearTransformPlotM2&comma;iterations&equals;10&comma;output&equals;animation

Determinant: .84
Norm:        1.206

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

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

ApplyLinearTransformPlotM2&comma;iterations&equals;10&comma;output&equals;animation&comma;trace&equals;4

Determinant: .84
Norm:        1.206

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

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

M3:=1.&comma;0.2&comma;0.3&verbar;0.3&comma;0.9&comma;0.3&verbar;0.2&comma;0.2&comma;1.&colon;

ApplyLinearTransformPlotM3&comma;grid&comma;output&equals;animation

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 >

See Also

plot/options, plot/typesetting, Student plot options, Student[LinearAlgebra], Student[LinearAlgebra][Operators]


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