Student[LinearAlgebra][ProjectionPlot] - plot the projection of a Vector onto a subspace
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Calling Sequence
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ProjectionPlot(V, S, opts)
ProjectionPlot(V, S, vars, opts)
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Parameters
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V
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Vector
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S
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Vector, list or set of Vectors, equation, or algebraic expression
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vars
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list of 2 or 3 variable names
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opts
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plotting options or equation(s) of the form option=value where option is one of showbasis, basisoptions, showcomplement, complementoptions, showlines, lineoptions, showprojection, projectionoptions, showsubspace, subspaceoptions, showvector, vectoroptions, or Student[plot options]; specify options for the plot
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Description
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The ProjectionPlot(V, S) command plots the projection of the 2- or 3-D Vector V onto the subspace defined by the parameter S.
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If the subspace S is defined by a Vector or set or list of Vectors, the subspace is taken to be the span of these Vectors. If S is an equation, the subspace is taken to be all vectors satisfied by that equation. A line or plane defined by an equation must pass through the origin. If S is given as an algebraic expression, it is treated as the equation .
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If an equation is used to define the line or plane (the subspace), a list of the variable names of the axes must be given. The list is not required when all axis variable names appear in the expression, in which case, they are sorted lexicographically if no order is given. For example, given the equation , the order chosen is .
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The opts argument can contain any of the Student plot options or any of the following equations that set plot options.
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showbasis = true or false
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Specifies whether the Vectors specified in the subspace parameter S are plotted. This option is ignored if S is given as an equation or algebraic expression. [Default: false]
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Provides options (such as color) used to plot the Vectors given in the parameter S. This option is ignored if S is given as an equation or algebraic expression. See plots[arrow] for further information.
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showcomplement = true or false
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Specifies whether the projection of the input Vector V onto the orthogonal complement of S is plotted. [Default: true]
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Provides options (such as color) used to plot the projection of V onto the orthogonal complement of S. See plots[arrow] for further information.
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showlines = true or false
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Specifies whether lines from the head of V to the heads of the projections of V onto the subspace S and its orthogonal complement are plotted. This option is subordinate to each of the showcomplement and showprojection options. [Default: true]
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Provides options (such as color, linestyle) used to plot the lines drawn from the head of V to the heads of the projections of V onto the subspace S and its orthogonal complement. See plot/options for further information.
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showprojection = true or false
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Specifies whether the projection of the input Vector V onto the subspace S is plotted. [Default: true]
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Provides options (such as color) used to plot the projection of V onto the subspace S. See plots[arrow] for further information.
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showsubspace = true or false
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Specifies whether the subspace defined by the parameter S is plotted. [Default: true]
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showvector = true or false
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Specifies whether the Vector being projected, V, is plotted. [Default: true]
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Provides options (such as color) used to plot the input Vector V. See plots[arrow] for further information.
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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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>
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>
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>
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Vector: <-2, 3>
Projection: <-2.776, 1.190>
Orthogonal complement: <.7759, 1.810>
Norm of orthogonal complement: 1.970
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Vector: <-3, 5, -3>
Projection: <-4.200, 1.400, -3.>
Orthogonal complement: <1.200, 3.600, 0.>
Norm of orthogonal complement: 3.795
Equation of the plane: x+3*y = 0
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The commands to create the plots from the Plotting Guide are
>
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Vector: <3, 2>
Projection: <1.324, -.7941>
Orthogonal complement: <1.676, 2.794>
Norm of orthogonal complement: 3.258
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Vector: <1, 2, 3>
Projection: <1.000, 2.500, 2.500>
Orthogonal complement: <.7971e-13, -.5000, .5000>
Norm of orthogonal complement: .7071
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