Integration over angular variables for two coupled matrices

International audience; An integral over the angular variables for two coupled $n$ x $n$ real symmetric, complex hermitian or quaternion self-dual matrices is expressed in term of the eigenvalues and eigenfunctions of a hamiltonian closely related to the Calogero hamiltinian. This generalizes the known result for the complex hermitian matrices. The integral can thus be evaluated for $n = 2$ and reduced to a single sum for $n = 3$