Tropical patterns of matrices and the Gondran-Minoux rank function

DOI10.1016/j.laa.2012.04.028zbMath1266.15038OpenAlexW2045541246MaRDI QIDQ445842

Yaroslav N. Shitov, Alexander E. Guterman

Publication date: 27 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.04.028

zbMATH Keywords

inequalitiesmatrix spacestropical rankdeterminantal rankGondran-Minoux rank functiontropical algebrastropical ring

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Miscellaneous inequalities involving matrices (15A45) Vector spaces, linear dependence, rank, lineability (15A03) Max-plus and related algebras (15A80)

Related Items (4)

Rank functions of tropical matrices ⋮ The complexity of tropical matrix factorization ⋮ Tropical lower bounds for extended formulations ⋮ The arctic rank of a Boolean matrix

Cites Work

• Unnamed Item
• Inequalities for Gondran-Minoux rank and idempotent semirings
• Signsolvability revisited
• Real rank versus nonnegative rank
• Sign-nonsingular matrices and even cycles in directed graphs
• Determinantal identities over commutative semirings
• Matrices with different Gondran-Minoux and determinantal ranks over MAX-algebras
• Graphs, dioids and semirings. New models and algorithms.
• Linear independence over tropical semirings and beyond
• The Even Cycle Problem for Directed Graphs
• Kapranov rank vs. tropical rank

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