Matrix Transform
Matrix Transform
[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]

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; it may also refer to them going home and seeing a shrink (counselor) in despair of their student understanding.
[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]
