Derivative principles for invariant ensembles

In the present work we show that joint probability distribution of eigenvalues can be expressed in terms a differential operator acting on some other matrix quantities. Those quantities might diagonal or pseudo-diagonal entries as it is case for Hermitian matrices. These representations are called derivative principles. We them additive spaces Hermitian, antisymmetric, anti-self-dual, and complex rectangular matrices well two multiplicative positive definite unitary all six cases prove uniqueness