In the previous chapter we briefly discussed the convergence of a single sequence of matrices in terms of the convergence of its ESD. When we have more than one sequence of matrices, how should their joint convergence be viewed? Then the most natural object to consider is the non-commutative ∗-probability space (NCP) generated by polynomials of these matrices and study the convergence of the elements of this space. Convergence of the spectral distribution of any given polynomial of matrices is closely related to the above convergence.