Linear preservers of extremes of rank inequalities over semirings: the factor rank

DOI10.1007/s10958-005-0451-1zbMath1127.15001OpenAlexW1972218839MaRDI QIDQ2462026

Leroy B. Beasley, Alexander E. Guterman

Publication date: 23 November 2007

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-005-0451-1

zbMATH Keywords

linear preserversemiringscolumn rankrow rankrank inequality

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Linear transformations, semilinear transformations (15A04) Semirings (16Y60) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Linear preservers of extremes of rank inequalities over semirings: Row and column ranks ⋮ Linear transformations of tropical matrices preserving the cyclicity index ⋮ Surjective linear transformations of tropical matrices preserving transitive closures ⋮ Linear preservers for matrices over a class of semirings ⋮ Linear isomorphisms preserving Green's relations for matrices over anti-negative semifields ⋮ Monotone linear transformations on matrices over semirings ⋮ Matrix Invariants over Semirings ⋮ Linear mappings preserving coincidence of factorized and boundary ranks of matrices over semirings ⋮ The characterization of operators preserving primitivity for matrix \(k\)-tuples ⋮ Extreme preservers of maximal column rank inequalities of matrix sums over semirings ⋮ Preserving regular tournaments and term rank-1 ⋮ Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings

Cites Work

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• Rank equalities related to outer inverses of matrices and applications
• Chapter 9: miscellaneous preserver problems
• RANK INEQUALITIES OVER SEMIRINGS
• When Does Rank(A+B)=Rank(A)+Rank(B)?
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• Boolean rank of Kronecker products

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