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A hermitian matrix can be parametrized by a set consisting of its determinantand the eigenvalues of its submatrices. We established a group of equationswhich connect these variables with the mixing parameters of diagonalization.These equations are simple in structure and manifestly invariant in form underthe symmetry operations of dilatation, translation, rephasing and permutation.When applied to the problem of neutrino oscillation in matter they produced twonew ``matter invariants" which are confirmed by available data.

Hermitian Matrix Diagonalization and its Symmetry Properties