Rotation in Three Dimensions - 3D Math Primer for Graphics and Game Development - page 294

9. Prove the statement made in Section 8.5.7: the magnitude of the product
of two quaternions is the product of the magnitudes.
10. Expand the multiplication qvq −1 , and verify that the matrix Equation (8.20)
is correct.
11. Make a survey of some game engines and open source code and figure out
the conventions regarding row/column vectors, rotation matrices, and Euler
angles.
I wear a necklace, cause I wanna know when I'm upside down.
— Mitch Hedberg (1968-2005)