The book was vague on this subject and as a result, everyone is in disagreement on this. All my friends think that the directions of the principal axes are the eigenvectors of the tensor of inertia wrt some Oxyz axes. I think that the directions of the principal axes are obtained by applying on the Oxyz axes the matrix R that diagonalizes the tensor of inertia. (i.e. the matrix whose lines are the eigenvectors of I) The T.A. thinks we're both right.