Given an inertia tensor of a rigid body I, one can always find a rotation that diagonalizes I as I = RT I0 R (let's say none of the value of the inertia in I0 equal each other, though). R is not unique, however, as one can always rotate 180 degrees about a principal axis, or rearrange the entries of I0 via rotations. I'm curious if there a set of conditions that one can impose on R to make it unique, however. One can eliminate the ordering issue by insisting that the entries of I0 are in sorted order. What about the 180 degree rotation issue, is there an additional condition that one can impose to eliminate this ambiguity?