Invariant measure on sums of symmetric 3*3 matrices with specified eigenvalues
Joe Repka, Norman J. Wildberger · Journal of Physics A Mathematical and General · 1990
Suppose A and B are symmetric 3*3 matrices. Rotate one of them by sigma in SO(3) and add; the eigenvalues of the resulting matrix A+B sigma vary over a set determined by the eigenvalues of A and B. In the case where one of A and B has a repeated eigenvalue the authors find the image of SO(3) Haar measure d sigma on this set, which describes the coupling of different rigid rotors.