Semiring rank versus column rank. (English) Zbl 0642.15002

Beasley, LeRoy B.; Pullman, Norman J.

Linear Algebra Appl. 101, 33-48 (1988).

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.

Keywords:

Schein rank; matrix over semiring; row rank; column rank

References:

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