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Boolean-rank-preserving operators and Boolean-rank-1 spaces. (English) Zbl 0536.20044

The authors prove that a Boolean linear operator from the set of \(n\times m\) Boolean matrices to itself \((m,n>1)\) preserves Boolean rank iff if preserves ranks 1, 2 iff it has the form UAV or \(UA^ tV\) for U, V permutation matrices. They also find the maximum cardinality and dimension of rank 1 subspaces of \(n\times m\) Boolean matrices.
Reviewer: K.-H.Kim

MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
15A04 Linear transformations, semilinear transformations
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References:

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