On perturbations of non-diagonalizable stochastic matrices of order 3

Pieter-Jan Pauwelyn, M. A. Guerry

Research output: Contribution to journalArticleScientificpeer-review


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.
Original languageEnglish
Article number108633
Number of pages6
JournalStatistics & probability letters
Publication statusPublished - Feb 2020
Externally publishedYes


  • Stochastic matrices
  • non-diagonalizable matrices
  • perturbation theory
  • Markov chains


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