Transforming a Unit Square

This worksheet is to accompany Section 1.9 - The Matrix of a Linear Transformation, in Lay's Linear Algebra

by Harry S. Mills

Based on visualization ideas (clouds of points) and techniques by Michael K. May and Russell Blyth.

I'd like to have a bunch of exercises for you, here, but for now, I'm content with the implementation the visualizations of transformations 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 that are given in the text.

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Warning, the name changecoords has been redefined

Warning, the assigned name arrow now has a global binding

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We show some examples of how Linear (Matrix) Transformations transform a unit square.

Build a "square cloud" of points:

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Square01 :={seq(Vector(2,[rand(0..100)()/100,rand(0..100)()/100]),i=1..100)}:

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The original square:

setofimages := {seq(Square01[i],i=1..100)} minus {0}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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Contraction of the square via action of the scalar matrix

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A:=Matrix(<< .5 | 0 >, < 0 | .5 >>): print(A); setofimages := {seq(A.Square01[i],i=1..100)}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

print();

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

The original square:

setofimages := {seq(Square01[i],i=1..100)} minus {0}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

Dilation of the square via action of the scalar matrix

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2OVEhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGOi8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUqbWF0aGNvbG9yR0ZDLyUvbWF0aGJhY2tncm91bmRHRkYvJStmb250ZmFtaWx5R0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKW1hdGhzaXplR0Y0

A:=Matrix(<< 2 | 0 >, < 0 | 2 >>): setofimages := {seq(A.Square01[i],i=1..100)}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

NiUtSSdQT0lOVFNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2YHE3JCQiKysrKysjKiEjNSQiKysrKys5Ri03JCQiKysrKyF5IiEiKiQiKysrK1M9RjM3JCQiKysrKytFRi0kIisrKysrKSpGLTckJCIrKysrUzlGMyQiKysrKyFvIkYzNyQkIisrKyshPSJGM0Y0NyRGMSQiKysrKytvRi03JEY8JCIrKysrUzxGMzckJCIrKysrK3NGLUZBNyQkIisrKysrISlGLSQiKysrKytnISM2NyQkRlBGLSQiKysrK2c1RjM3JCQiKysrKz89RjMkRi9GMzckJCIrKysrK09GLSQiKysrKys9Ri03JCQiKysrKysnKUYtJCIrKysrK0NGLTckJCIrKysrKz9GUSQiKysrKytxRi03JCQiKysrKz88RjMkIisrKysrbUYtNyQkIisrKytnOUYzJCIrKysrKycqRi03JCQiKysrKytTRlEkIisrKytTPkYzNyQkIiIhRmRwJCIrKysrIVEiRjM3JEY8JCIrKysrK1VGLTckJCIrKysrK0dGLSQiKysrKytdRi03JEZBJCIrKysrZzhGMzckJCIrKysrKykpRi0kIisrKys/OEYzNyQkIisrKysraUYtRmBwNyQkIisrKys/NUYzJCIrKysrUzZGMzckJCIrKysrK2VGLSQiKysrKys1Ri03JEYxRmlvNyQkIisrKyshKT5GMyQiKysrKytZRi03JEZlcSQiKysrKys7RjM3JEZTRltzNyRGZG8kIisrKysrSUYtNyQkIisrKytTN0YzJCIrKysrK3lGLTckJCIrKysrPzpGMyQiKysrKyt3Ri03JCQiKysrKyFbIkYzRl5wNyQkIisrKys/OUYzRjE3JEZlcSQiKysrK2c2RjM3JCRGXHNGLSQiKysrK2c3RjM3JEZgcUZecDckRmV0JCIrKysrK0FGLTckRiskIisrKysrYUYtNyQkIisrKysrdUYtRmBxNyRGW3IkIisrKysrW0YtNyRGXXJGNDckJCIrKysrK01GLSQiKysrKyslKUYtNyQkIisrKysrNkYzRml1NyRGam5GZnI3JCQiIiJGZHBGXnA3JEY+RmV0NyRGW3FGZnQ3JEZkc0ZZNyRGYnRGX3M3JEZfdEZfbzckJCIrKysrIUciRjNGYHE3JCQiKysrKytfRi0kIisrKysrPkYzNyQkIisrKytnPUYzRltyNyRGaHFGZHM3JEYxRmZvNyQkRk5GUSRGYG9GLTckJCIrKysrKyEqRi1Gam43JEYxRl5wNyRGXXdGZnc3JEZldEZnczckJCIrKysrK0tGLUZlcDckRmBwRmZ3NyQkIisrKytTO0YzRmN1NyQkIisrKysra0YtRmByNyRGW3AkIiIjRmRwNyRGXnhGaHg3JEZlcSQiKysrK1M6RjM3JEZldCQiKysrK1M1RjM3JCQiKysrK1M4RjNGYng3JEZkcyQiKysrKys4RjM3JEZfcyQiKysrKytjRi03JCQiKysrKys3RjMkIisrKytnO0YzNyRGSkZcdDckRl13RmB3NyRGaHIkIisrKyshZSJGMzckRmBwRmJ0NyQkIisrKyshMyJGM0ZkczckRmd1RltyNyRGZXlGanQ3JEY0RmNxNyRGW3JGW3M3JEZPJEZobkYzNyRGX3lGW3o3JEZceSQiKysrKytXRi03JEZgW2xGTTckRmVxRmh4NyRGXXdGYnI3JEZocEZkczckRmBwRml1NyRGW3dGYHA3JEZqdEZlbjckRmVwRmFvNyRGYnNGZnI3JEZoeEZpbzckRmNwRmJ4NyRGYHZGX3k3JEZbcEZbcDckRmFvRmduNyRGLkZicy1JJVZJRVdHRiU2JDskISIkRmRwJCIiJEZkcEZkXGwtSSdDT0xPVVJHRiU2JkkkUkdCR0YlRmRwRmRwRmRw

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

print();

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

The original square:

setofimages := {seq(Square01[i],i=1..100)} minus {0}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

Contraction followed by a shear transformation of the square via action of the scalar matrix

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiYtSSNtaUdGJTY5USJBRigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRigvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOy8lKXJlYWRvbmx5R0Y4LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYoLyUqbWF0aGNvbG9yR0ZELyUvbWF0aGJhY2tncm91bmRHRkcvJStmb250ZmFtaWx5R0YyLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y1LUkjbW9HRiU2M1EiPUYoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRigvJSdyc3BhY2VHRltwLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lMGZvbnRfc3R5bGVfbmFtZUdGWC8lJXNpemVHRjUvJStmb3JlZ3JvdW5kR0ZELyUrYmFja2dyb3VuZEdGRy1GJDYlLUYtNjlRIUYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLUYkNiUtRl9vNjNRIltGKC9GY29RJ3ByZWZpeEYoL0Zmb0Y7RmdvL0Zqb1EudGhpbm1hdGhzcGFjZUYoL0ZdcEZkci9GX3BGO0ZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1GJDYlRmhxLUknbXRhYmxlR0YlNiQtSSRtdHJHRiU2JC1JJG10ZEdGJTYjLUYkNiQtRl9vNjNRIi5GKEZib0Zlb0Znby9Gam9RJDBlbUYoL0ZdcEZoc0ZecEZgcEZicEZlcEZocEZqcEZccUZecUZgcUZicUZkcS1JI21uR0YlNjlRIjVGKEYwRjNGNi9GOkY4RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbi9Gam5RJ25vcm1hbEYoRlxvLUZgczYjLUZbdDY5USIwRihGMEYzRjZGXnRGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRl90RlxvLUZdczYkRmF0Rl9zRmhxLUZfbzYzUSJdRigvRmNvUShwb3N0Zml4RihGYnJGZ29GY3IvRl1wUTJ2ZXJ5dGhpbm1hdGhzcGFjZUYoRmZyRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxRmhxLUZfbzYzUSI6RihGYm9GZW9GZ29GaW9GXHBGXnBGYHBGYnBGZXBGaHBGanBGXHFGXnFGYHFGYnFGZHE3I0MkL0kiQUdGKC1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0YqNiMvSSQlaWRHRigiKilRWjk6ISIi

A:=Matrix(<< .5 | 0 >, < 0 | .5 >>): B:=Matrix(<< 1 | 0 >, < 2.5 | 1 >>): setofimages := {seq(B.A.Square01[i],i=1..100)}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtRiQ2JS1JI21vR0YlNjNRIltGKC8lJWZvcm1HUSdwcmVmaXhGKC8lJmZlbmNlR1EldHJ1ZUYoLyUqc2VwYXJhdG9yR1EmZmFsc2VGKC8lJ2xzcGFjZUdRLnRoaW5tYXRoc3BhY2VGKC8lJ3JzcGFjZUdGPS8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y6LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lJXNpemVHUSMxMkYoLyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GKC1GJDYjLUknbXRhYmxlR0YlNiQtSSRtdHJHRiU2JC1JJG10ZEdGJTYjLUkjbW5HRiU2OVEiMkYoLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR0ZVLyUlYm9sZEdGOi8lJ2l0YWxpY0dGOi8lKnVuZGVybGluZUdGOi8lKnN1YnNjcmlwdEdGOi8lLHN1cGVyc2NyaXB0R0Y6LyUrZm9yZWdyb3VuZEdGWC8lK2JhY2tncm91bmRHRmVuLyUnb3BhcXVlR0Y6LyUrZXhlY3V0YWJsZUdGOi8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjovJSpjb252ZXJ0ZWRHRjovJStpbXNlbGVjdGVkR0Y6LyUscGxhY2Vob2xkZXJHRjovJTBmb250X3N0eWxlX25hbWVHRlIvJSptYXRoY29sb3JHRlgvJS9tYXRoYmFja2dyb3VuZEdGZW4vJStmb250ZmFtaWx5R0Znby8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRigvJSltYXRoc2l6ZUdGVS1GX282Iy1GYm82OVEiMEYoRmVvRmhvRmpvRlxwRl5wRmBwRmJwRmRwRmZwRmhwRmpwRlxxRl5xRmBxRmJxRmRxRmZxRmhxRmpxRlxyRl5yRmFyLUZcbzYkRmNyRl5vLUYvNjNRIl1GKC9GM1EocG9zdGZpeEYoRjVGOEY7L0Y/UTJ2ZXJ5dGhpbm1hdGhzcGFjZUYoRkBGQkZERkdGSkZMRk5GUEZTRlZGWS1GLzYzUSIsRigvRjNRJmluZml4RigvRjZGOi9GOUY3L0Y8USQwZW1GKC9GP1EzdmVyeXRoaWNrbWF0aHNwYWNlRigvRkFGOkZCRkRGR0ZKRkxGTkZQRlNGVkZZLUYkNiVGLi1GJDYjLUZpbjYkLUZcbzYkRmNyLUZfbzYjLUZibzY5USkmbWludXM7MUYoRmVvRmhvRmpvRlxwRl5wRmBwRmJwRmRwRmZwRmhwRmpwRlxxRl5xRmBxRmJxRmRxRmZxRmhxRmpxRlxyRl5yRmFyLUZcbzYkLUZfbzYjLUZibzY5RklGZW9GaG9Gam9GXHBGXnBGYHBGYnBGZHBGZnBGaHBGanBGXHFGXnFGYHFGYnFGZHFGZnFGaHFGanFGXHJGXnJGYXJGY3JGanI3Iy1fRilJLG1wcmludHNsYXNoR0YoNiQ3JC1JJ1JUQUJMRUdGKDYlIio7IypvXyItSSdNQVRSSVhHRig2IzckNyQiIiMiIiE3JEZgdkZfdkknTWF0cml4RzYkJSpwcm90ZWN0ZWRHRiotRmd1NiUiKispcFM6LUZbdjYjNyQ3JEZgdiEiIjckIiIiRmB2RmJ2NyQtRmJ2NiMvSSQlaWRHRihGaXUtRmJ2NiMvRmN3Rmd2

print();

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2OVEhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGOi8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUqbWF0aGNvbG9yR0ZDLyUvbWF0aGJhY2tncm91bmRHRkYvJStmb250ZmFtaWx5R0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKW1hdGhzaXplR0Y0

The original square:

setofimages := {seq(Square01[i],i=1..100)}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

A shear transformation:

A:=Matrix(<< 1 | 2 >, < 0 | 1 >>): setofimages := {seq(A.Square01[i],i=1..100)}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

Now we do some rotations through an angle \317\206:

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

The original square:

setofimages := {seq(Square01[i],i=1..100)} minus {0}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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

Rotation by 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 radians:

phi:=-Pi/4: setofimages := {seq(RotationMatrix.Square01[i],i=1..100)}: pointplot(setofimages,view=[-3..3,-3..3],color=black);

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