  We employ Dirac's bra-ket notation to define the inertia tensor operator that
is independent of the choice of bases or coordinate system. The principal axes
and the corresponding principal values for the elliptic plate are determined
only based on the geometry. By making use of a general symmetric tensor
operator, we develop a method of diagonalization that is convenient and
intuitive in determining the eigenvector. We demonstrate that the bra-ket
approach greatly simplifies the computation of the inertia tensor with an
example of an $N$-dimensional ellipsoid. The exploitation of the bra-ket
notation to compute the inertia tensor in classical mechanics should provide
undergraduate students with a strong background necessary to deal with abstract
quantum mechanical problems.
