Inverse elementary divisor problem for nonnegative matrices
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- by Henryk Minc PDF
- Proc. Amer. Math. Soc. 83 (1981), 665-669 Request permission
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
- Abraham Berman and Robert J. Plemmons, Nonnegative matrices in the mathematical sciences, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 544666 F. R. Gantmacher, The theory of matrices, Vol. 2, Chelsea, New York, 1959.
- Henryk Minc, Inverse elementary divisor problem for doubly stochastic matrices, Linear and Multilinear Algebra 11 (1982), no. 2, 121–131. MR 650726, DOI 10.1080/03081088208817437
Additional Information
- © Copyright 1981 American Mathematical Society
- 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