We considered motion of a rigid body, when 1 point in the body (which we take to be the origin O) is fixed. Then the most general motion of the rigid body is rotation about some axis through O.
We calculated the angular momentum relative to O of such a rotation,
relating it to the angular frequency of the rotation by introducing
the inertia tensor I. We derived I by requiring 
, where I acts on the column vector 
by
matrix multiplication. We explicitly showed entries of the 3 by 3
matrix I, and discussed generalizations from discrete to continuous
rigid bodies. We noted how I transforms under a change of basis
(rotation of the body axes), and noted that because I is not
proportional to the identity matrix, the angular momentum vector
in general does not point in the same direction as the
rotation axis 
.
--
KB