On perturbations of non-diagonalizable stochastic matrices of order 3

P.J. Pauwelyn and M.A. Guerry

Statistics & Probability Letters, 2020, vol. 157, issue C

Abstract: We show that it is possible for every non-diagonalizable stochastic 3 × 3 matrix to be perturbed into a diagonalizable stochastic matrix with the eigenvalues, arbitrarily close to the eigenvalues of the original matrix, with the same principal eigenspaces. An algorithm is presented to determine a perturbation matrix, which preserves these spectral properties. Additionally, a relation is proved between the eigenvectors and generalized eigenvectors of the original matrix and the perturbed matrix.

Keywords: Stochastic matrices; Non-diagonalizable matrices; Perturbation theory; Markov chains (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108633

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