Images of Parallelograms Under Linear Transformations

> with(linalg):

Warning, the protected names norm and trace have been redefined and unprotected

Load functions to visualize the effects of linear transformations.
You may need to customize the following path to your environment.

> read `C:/othermaple/pargrm_image.txt`;

Warning, the name changecoords has been redefined

Basic Usage is:

gr := plot_pargrm_2d([ v1, v2 ], A)


where v1 and v2 are vectors in R^2 and A is a 2 by 2 matrix.

The parallelogram with vertices 0, v1, v1+v2, and v2 is drawn in blue.

The parallelogram with vertices 0, Av1, A(v1+v2), and Av2 is drawn in red.

There is also a function


describing the 3 dimensional case.

> vec3 := vector([1,0]);

vec3 := vector([1, 0])

> vec4 := vector([0,1]);

vec4 := vector([0, 1])

> A := matrix(2,2,[.1,.1,.1,-.1]);

A := matrix([[.1, .1], [.1, -.1]])

This command computes the drawing of one parallelogram.

> gr1 := plot_pargrm_2d([vec3,vec4],red,2):

This actually displays it.

> display(gr1);

[Maple Plot]

This computes a graphic structure for both the original and image parallelogram.

> gr2 := pargrm_image_2d([vec3,vec4],A):

Display it.

> display(gr2,scaling=constrained);

[Maple Plot]