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Another Remark on a Result of K. Goldberg
Published online by Cambridge University Press: 20 November 2018
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In [3] K. Goldberg showed that if A is a 0-1 matrix that satisfies
(1.1)
then for some permutation matrix P, PAP* is a direct sum of matrices each of which is either zero or consists only of ones. More recently J. L. Brenner [1] proved that if A ∦ 0 (i.e. A has non-negative entries) and satisfies (1) then there exists a permutation matrix P such that PAP* = A1⊕ … ⊕An in in which each Ai is either 0 or all positive, Ai > 0, and satisfies (1) as well.
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- Copyright © Canadian Mathematical Society 1963
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