The matrix is the Cartesian representation of the mass moment of inertia tensor, which will be explored further in §B.4.15 below.
In summary, the angular momentum vector is given by the mass moment of inertia tensor times the angular-velocity vector representing the axis of rotation.
Note that the angular momentum vector does not in general point in the same direction as the angular-velocity vector . We saw above that it does in the special case of a point mass traveling orthogonal to its position vector. In general, and point in the same direction whenever is an eigenvector of , as will be discussed further below (§B.4.16). In this case, the rigid body is said to be dynamically balanced.B.24
Relation of Angular to Linear Momentum