184: Matrix Transform
Title text: In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.
A 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. 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.
- [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:
- [An equal sign]
- [The same two by one matrix, but rotated by 90 degrees clockwise: