  We work over a field K of characteristic zero. The Poincare series for the
algebra C_{n,2} of GL_n-invariants and the algebra T_{n,2} of GL_n-concomitants
of two generic n x n matrices x and y are presented for n less than or equal 6.
Both simply graded and bigraded cases are included. The cases for n at most 4
were known previously. If n=5 or 6, we show that C_{n,2} has no bigraded system
of parameters. For the algebra C_{4,2} and C_{5,2} we construct a minimal set
of generators and give an application to Specht's theorem on unitary similarity
of two complex matrices. Five conjectures are proposed concerning the
numerators and denominators of various Poincare series mentioned above. Some
heuristic formulas and open problems are stated.
