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A Remark on a Result of Marvin Marcus
Published online by Cambridge University Press: 20 November 2018
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Marcus [2] has proved the following theorem.
Suppose A is a non-negative normal matrix satisfying p(A) = 0 in which p(λ) is a monic polynomial no two of whose non-zero roots have the same modulus. Then there exists a permutation matrix P such that PAP* is a direct sum, PAP* = A1 ⊕ A2 ⊕ … ⊕ Am, in which each Ai is either O or primitive.
This note gives a generalisation of this result, dropping the non-negative assumption and weakening the normality assumption.
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- Research Article
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- Copyright
- Copyright © Canadian Mathematical Society 1963
References
1.
Dulmage, A. L. and Mendelsohn, N. S. "The Characteristic Equation of an Imprimitive Matrix". Submitted to the Journal of S. I. A. M.Google Scholar
2.
Marcus, Marvin "Another Remark on a Result of K. Goldberg". Can. Math. Bull. 6 (1963). p. 7.10.4153/CMB-1963-002-6Google Scholar
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