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• W3149741176 abstract "In Markov chain theory, stochastic matrices are used to describe inter-state transitions. Powers of such transition matrices are computed to determine the behaviour within a Markov system. For this, diagonalizable matrices are preferred because of their useful properties. The non-diagonalizable matrices are therefore undesirable. The aim is to determine a nearby diagonalizable matrix A~, starting from a non-diagonalizable matrix A. Previous studies tackled this problem, limited to 3×3 stochastic matrices. In this paper, these results are generalized for n×n stochastic matrices. Spectral properties of A are preserved in this process, such that A and A~ have coinciding semisimple eigenvalues and coinciding corresponding eigenvectors. This problem is examined and solved in this study and an algorithm is presented to find such a diagonalizable matrix A~." @default.
• W3149741176 created "2021-04-13" @default.
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• W3149741176 date "2021-03-24" @default.
• W3149741176 modified "2023-09-27" @default.
• W3149741176 title "Perturbations of non-diagonalizable stochastic matrices with preservation of spectral properties" @default.
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• W3149741176 doi "https://doi.org/10.1080/03081087.2021.1904813" @default.
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