We present a direct solution to the problem of constructing a stochastic
matrix with prescribed eigenspectrum, widely referred to as the
stochastic inverse eigenvalue problem. The solution uses Markov state
disaggregation to construct a Markov chain with stochastic transition
matrix possessing the required eigenspectrum. Existing solutions that
follow the same approach are limited to constructing matrices with
real-valued eigenspectra only. The novel solution directly constructs
matrices with complex-valued eigenspectra by applying a new
disaggregation technique in tandem with a technique from a previous
solution. Due to this generalization, the novel solution is able to
successfully model physical systems from a larger family. Furthermore,
the novel solution constructs the matrix in a finite and predetermined
number of iterations, and without numerical approximation. The solution
is demonstrated by deriving an expression for a set of 4 x 4 stochastic
matrices sharing the same prescribed complex-valued eigenspectrum and
indexed by a real parameter.