Semiring rank versus column rank

DOI10.1016/0024-3795(88)90141-3zbMath0642.15002OpenAlexW2088450772WikidataQ105890738 ScholiaQ105890738MaRDI QIDQ1101524

Norman J. Pullman, Leroy B. Beasley

Publication date: 1988

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90141-3

zbMATH Keywords

column rankrow rankSchein rankmatrix over semiring

Mathematics Subject Classification ID

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

Related Items (27)

Linear preservers of extremes of rank inequalities over semirings: Row and column ranks ⋮ Rank functions of tropical matrices ⋮ Rank comparisons ⋮ Linear operators that preserve column rank of fuzzy matrices ⋮ On the coincidence of the factor and Gondran-Minoux rank functions of matrices over a semiring ⋮ Maximal rank-one spaces of matrices over chain semirings. I: u-spaces ⋮ Separability of distinct Boolean rank-1 matrices ⋮ Unnamed Item ⋮ The augmentation property of binary matrices for the binary and Boolean rank ⋮ A comparison of nonnegative real ranks and their preservers ⋮ Linear operators that preserve maximal column rank of boolean matrices^* ⋮ Boolean rank of upset tournament matrices ⋮ Ranks of fuzzy matrices. Applications in state reduction of fuzzy automata ⋮ Factorizations of matrices over semirings. ⋮ The complexity of tropical matrix factorization ⋮ Tan's epsilon-determinant and ranks of matrices over semirings ⋮ Standard Bases of a Vector Space Over a Linearly Ordered Incline ⋮ Linear preservers of extremes of rank inequalities over semirings: the factor rank ⋮ Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations ⋮ Spanning column ranks and their preservers of nonnegative matrices ⋮ Linear Operators That Preserve Column Rank of Boolean Matrices ⋮ On tropical matrices of small factor rank ⋮ Column ranks and their preservers over nonnegative real matrices. ⋮ Matrix Invariants over Semirings ⋮ Extreme preservers of maximal column rank inequalities of matrix sums over semirings ⋮ Real rank versus nonnegative rank ⋮ Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings

Cites Work

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• Fuzzy rank-preserving operators
• Primes in the semigroup of Boolean matrices
• On generalized inverses of boolean matrices. II
• On generalized inverses of Boolean matrices
• Primes in the semigroup of non-negative matrices

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