Toeplitz matrices generated by the Laurent series expansion of an arbitrary rational function

Let ${T_n}(f) = ({a_{i - j}})_{i,j = 0}^n$ be the finite Toeplitz matrices generated by the Laurent expansion of an arbitrary rational function. An identity is developed for $\det ({T_n}(f) - \lambda )$ which may be used to prove that the limit set of the eigenvalues of the ${T_n}(f)$ is a point or consists of a finite number of analytic arcs.