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Semiring rank versus column rank. (English) Zbl 0642.15002

For matrices over a semiring (Schein) rank, row rank, and column rank can all be different. The authors compute the largest rank, such that for all matrices of at most that rank, rank, row rank, and column rank are all equal for specified matrix sizes for many semirings including Boolean, fuzzy, \(Q^+\), \(Z^+\).
Reviewer: K.H.Kim

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
15B48 Positive matrices and their generalizations; cones of matrices
15A03 Vector spaces, linear dependence, rank, lineability
20M20 Semigroups of transformations, relations, partitions, etc.
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References:

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