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## Main Question or Discussion Point

Given an inertia tensor of a rigid body I, one can always find a rotation that diagonalizes I as I = R

^{T}I_{0}R (let's say none of the value of the inertia in I_{0}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 I_{0}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 I_{0}are in sorted order. What about the 180 degree rotation issue, is there an additional condition that one can impose to eliminate this ambiguity?