  A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric
dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise
orthogonal ranges. This determines a representation of the Cuntz-Toeplitz
algebra. When $A$ acts on a finite dimensional space, the \wot-closed
nonself-adjoint algebra $\mathfrak{S}$ generated by $S$ is completely described
in terms of the properties of $A$. This provides complete unitary invariants
for the corresponding representations. In addition, we show that the algebra
$\mathfrak{S}$ is always hyper-reflexive. In the last section, we describe
similarity invariants. In particular, an $n$-tuple $B$ of $d\times d$ matrices
is similar to an irreducible $n$-tuple $A$ if and only if a certain finite set
of polynomials vanish on $B$.
