Editing 184: Matrix Transform

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==Explanation==
 
==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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A {{w|Rotation matrix|rotational matrix transformation}} (i.e. the big brackets with a few "cos" and "sin" in them) is used in computer graphics to rotate an image. The product of the transform matrix and the argument vector (a1, a2) is a rotated version of the argument vector, which should be noted as (a1', a2').
  
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The joke is that the author performed the rotation transformation on the notation rather than on the vector it represents.  
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The joke is that the author turned the image of the vector rather than writing the correct answer. Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including shrinking them. In this case the matrix would rotate the image 90 degrees clockwise.
  
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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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At the title text we see that the professors even shrinking at home on this joke.
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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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The red text in ''[[xkcd: volume 0]]'' notes that mean people wrote into state that the direction of rotation was wrong, but that's due to readers not checking the signs. Rather, the actual typo was that "shrink" in the title-text should have been "drink", but was left because of (1/2)[a1, a2].
 
  
 
==Transcript==
 
==Transcript==
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: cos90°    sin90°
 
: cos90°    sin90°
 
: -sin90°  cos90°]
 
: -sin90°  cos90°]
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:[Two by one matrix:]
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:[Two by one matrix:
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: [a₁
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: a₁
 
: a₂]
 
: a₂]
 
:[An equal sign]
 
:[An equal sign]
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:[The same two by one matrix, but rotated by 90 degrees clockwise:]
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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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: a₁
 
: a₂]
 
: a₂]
  
 
{{comic discussion}}
 
{{comic discussion}}
 
[[Category:Math]]
 
[[Category:Math]]

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