In this paper we outline a procedure which can be seen as an approximation to the well known “hopeless” problem of ifying $m$-tuples ($m \geq 2$) of $n \times n$ matrices under simultaneous conjugation by $GL_n$. The method relies on joint work with C. Procesi, on the étale local structure of matrix-invariants and recent work on the nullcone of quiver-representations.