Constructing a Minimal Basis of Invariants for Differential Algebra of Matrices.

We construct a basis of invariants for the set of second-order matrices consisting of the original matrix and its derivatives. It is shown that the presence of derivatives imposes connections on the elements of this set and reduces the number of elements in the basis compared to the purely algebraic case. Formulas for calculating algebraic invariants of such a set are proved. We state a generalization of Fricke's formulas in terms of the traces of the product of matrices in this set. [ABSTRACT FROM AUTHOR]