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Inverse elementary divisor problem for nonnegative matrices


Author: Henryk Minc
Journal: Proc. Amer. Math. Soc. 83 (1981), 665-669
MSC: Primary 15A18; Secondary 15A48
DOI: https://doi.org/10.1090/S0002-9939-1981-0630033-X
MathSciNet review: 630033
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Abstract: Given a diagonalizable positive matrix $ A$, there exists a positive matrix with the same spectrum as $ A$, and with arbitrarily prescribed elementary divisors, provided that elementary divisors corresponding to nonreal eigenvalues occur in conjugate pairs. It is also shown that a similar result holds for doubly stochastic matrices.


References [Enhancements On Off] (What's this?)

  • [1] Abraham Berman and Robert J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press, New York, 1979. MR 544666 (82b:15013)
  • [2] F. R. Gantmacher, The theory of matrices, Vol. 2, Chelsea, New York, 1959.
  • [3] Henryk Minc, Inverse elementary divisor problem for doubly stochastic matrices, Linear and Multilinear Algebra (to appear). MR 650726 (84h:15024)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0630033-X
Article copyright: © Copyright 1981 American Mathematical Society

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