Difference between revisions of "184: Matrix Transform"

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| number    = 184
 
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| date      = November 15, 2006
 
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| title    = Matrix Transform
 
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| image    = matrix_transform.png
 
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| titletext = In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.
 
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}}
 
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==Explanation==
 
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A {{w|Rotation matrix|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].
 
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The joke is that the author performed the rotation transformation on the image of the vector rather than just the vector itself.
 
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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.
 
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So the title text may be referring to the professors going home (translation) and shrinking (scaling) from the joke; it may also refer to them going home and seeing a shrink (counselor) in despair of their student understanding.
 
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==Transcript==
 
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:[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.]
 
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:[Square matrix:
 
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: cos90°    sin90°
 
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: -sin90°  cos90°]
 
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:[Two by one matrix:]
 
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: [a₁
 
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: a₂]
 
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:[An equal sign]
 
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:[The same two by one matrix, but rotated by 90 degrees clockwise:]
 
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: [a₁
 
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: a₂]
 
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{{comic discussion}}
 
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[[Category:Math]]
 

Revision as of 23:30, 4 May 2022

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