Subdiscriminants of a symmetric matrix and Jacobians of its invariant mappings

We present expressions for subdiscriminants of a symmetric matrix using sums of squares of the Jacobians of some invariant mappings of the matrix. We give simple and rather general sufficient conditions on these mappings under which they generate all subdiscriminants, including the discriminant. In particular, the subdiscriminants can be generated in this way by the system of all invariants of a symmetric matrix, that is, by the coefficients of its characteristic polynomial.
Bibliography: 10 titles.