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Published online by Cambridge University Press: 20 November 2018
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.