Editing 184: Matrix Transform
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==Explanation== | ==Explanation== | ||
− | 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 | + | 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]. |
− | The joke is that the author performed the rotation transformation on the | + | 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. | + | 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 | + | 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 in despair of their student understanding. |
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==Transcript== | ==Transcript== |