184: Matrix Transform

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Matrix Transform
In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.
Title text: In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.

Explanation[edit]

A rotational matrix transformation (i.e. the big brackets with "cos" and "sin" in them) is used in computer graphics to rotate an image. In general, to rotate a point [a1, a2] in a 2D space by z° clockwise, you can multiply it by the rotation matrix [cos z°, sin z°; -sin z°, cos z°]. In this case, the left side of the equation is rotating [a1, a2] by 90°. Simplifying the trigonometry, the 90° clockwise rotation matrix is [ 0, 1; -1, 0], so multiplying this by [a1, a2], you should get [a2, -a1].

The joke is that the author performed the rotation transformation on the image of the vector rather than just the vector itself.

Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including the other two affine transformations of scaling them or translating (moving) them. On a pedantic note, normally mathematics uses counterclockwise as a default, although computer graphics frequently use a clockwise default, so this may be an intentional reference.

So the title text may be referring to the professors going home (translation) and shrinking (scaling) from the joke.

Transcript[edit]

[A square matrix next to a vertical two-by-one matrix, equated to a horizontal matrix that looks like the two-by-one matrix turned 90 degrees.]
[Square matrix:
cos90° sin90°
-sin90° cos90°]
[Two by one matrix:]
[a₁
a₂]
[An equal sign]
[The same two by one matrix, but rotated by 90 degrees clockwise:]
[a₁
a₂]


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Discussion

This baby needs a bit more rigor. --Quicksilver (talk) 05:23, 24 August 2013 (UTC) 173.245.62.84 07:54, 7 April 2014 (UTC) I think this is also a reference to the movie "The Matrix", specifically the now famous scene where Neo does 90degree back bending to dodge bullets. 173.245.62.84 07:54, 7 April 2014 (UTC)

Maybe another reference: They'll go home (translation matrix) and shrink (scale matrix). Translation, scale and rotate are probably the most popular linear transformations. 108.162.218.89 23:39, 14 May 2014 (UTC)

I've been teach that the rotation was anticlockwise. Do computer turn the other way round that math teachers? by the way (left ( matrix{0 # 1 ## -1 # 0} right )*left ( binom 1 0 right)=left (binom 0 1 right) if you know what i mean. get fun. Yomismo (talk) 09:28, 18 March 2015 (UTC)