A direct solution to the stochastic inverse eigenvalue problem for complex-valued eigenspectra

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