After working quite well for some years, unfortunately the audio jack of my iPod Video broke down some time ago, only giving sound in one ear. Luckily, you can solve this for under $5 by buying an adapter to plug into the iPod’s connector and installing the Rockbox firmware on the iPod.
Problem
The trace algebra of two matrices is the polynomial ring generated by the traces of products of matrices A and B, like Tr(A), Tr(B), Tr(A.B), Tr(A.A), Tr(A.A.B.A.B). It is known that this trace algebra is the complete set of polynomials that are invariant under simultaneous conjugation of A and B (ie, if one replaces A and B by T^(-1).A.T and T^(-1).B.T, respectively, then the value of the polynomial doesn’t change).