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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)262-282
Journal / PublicationLinear Algebra and Its Applications
Online published11 Nov 2022
Publication statusPublished - 1 Feb 2023


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.

Research Area(s)

  • Inverse eigenvalue problem, Inverse stochastic problem, Markov state disaggregation, Stochastic matrix