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Diagonalizability of matrices over a principal ideal domain

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Ukrainian Mathematical Journal Aims and scope

A square matrix is said to be diagonalizable if it is similar to a diagonal matrix. We establish necessary and sufficient conditions for the diagonalizability of matrices over a principal ideal domain.

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References

  1. R. B. Richter and W. P. Wardlaw, “Diagonalization over commutative rings,” Am. Math. Monthly, 97, No. 3, 223–227 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Prokip, “On similarity of matrices over commutative rings,” Linear Alg. Appl., 399, 225–233 (2005).

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  3. V. M. Prokip, “Diagonalization of matrices over a principal ideal domain with minimal polynomial m (λ) = (λ − α)(λ − β), α ≠ β, ” Ukr. Mat. Visn., 7, No. 2, 212–219 (2010).

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  4. A. Steger, “Diagonability of idempotent matrices,” Pacif. J. Math., 19, No. 3, 535–542 (1969).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 2, pp. 283–288, February, 2012.

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Prokip, V.M. Diagonalizability of matrices over a principal ideal domain. Ukr Math J 64, 316–323 (2012). https://doi.org/10.1007/s11253-012-0649-6

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  • DOI: https://doi.org/10.1007/s11253-012-0649-6

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