@article{c5bfafe04c0646fa8e0ee0a6e6150be7, title = "A direct solution to the stochastic inverse eigenvalue problem for complex-valued eigenspectra", abstract = "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 the associated stochastic transition matrix possessing the required eigenspectrum. Existing solutions that follow the same approach are limited to constructing matrices with real-valued eigenspectra. 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 4×4 stochastic matrices sharing the same prescribed complex-valued eigenspectrum and indexed by a real parameter.", keywords = "Inverse eigenvalue problem, Inverse stochastic problem, Markov state disaggregation, Stochastic matrix", author = "McDonald, {Andr{\'e} M.} and {van Wyk}, {Micha{\"e}l A.} and Guanrong Chen", year = "2023", month = feb, day = "1", doi = "10.1016/j.laa.2022.11.005", language = "English", volume = "658", pages = "262--282", journal = "Linear Algebra and Its Applications", issn = "0024-3795", publisher = "Elsevier Inc.", }