Mathematical Sciences: The Invariants of n x n Matrices

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The project supported concerns the ring of invariants, C(n,r), of a set of r generic nxn matrices over a field K and the trace ring, R(n,r). The main problem is to find presentations for C(n,r) as an algebra over K and R(n,r) as an algebra over C(n,r). The project will also consider the minimal degree of elements in a generating set and whether the quotient field of C(n,r) is purely transcendental over K. The research supported concerns matrix theory, ring theory and the calculation of invariants. In particular, this involves an old problem of determining what mathematical functions are preserved under various transformations. This is of interest in many areas of science as well as in mathematics.