Real rank versus nonnegative rank

DOI10.1016/j.laa.2009.02.034zbMath1185.15002OpenAlexW2066019014MaRDI QIDQ1039742

Leroy B. Beasley, Thomas J. Laffey

Publication date: 23 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.02.034

zbMATH Keywords

polynomial matricesrankmatrix factorizationnonnegative integer matrices

Mathematics Subject Classification ID

Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (22)

Extended formulations for convex heptagons ⋮ Heuristics for exact nonnegative matrix factorization ⋮ Studying Non-negative Factorizations with Tools from Linear Algebra over a Semiring ⋮ Extension complexity of low-dimensional polytopes ⋮ Completely positive factorizations associated with Euclidean distance matrices corresponding to an arithmetic progression ⋮ Nonnegative rank of a matrix with one negative eigenvalue ⋮ Approximate nonnegative rank is equivalent to the smooth rectangle bound ⋮ Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks ⋮ On \(\epsilon\)-sensitive monotone computations ⋮ Symmetric nonnegative matrix trifactorization ⋮ On the nonnegative rank of distance matrices ⋮ Tropical patterns of matrices and the Gondran-Minoux rank function ⋮ Semi-nonnegative rank for real matrices and its connection to the usual rank ⋮ Euclidean distance matrices and separations in communication complexity theory ⋮ On the linear extension complexity of regular \(n\)-gons ⋮ Nonnegative rank factorization -- a heuristic approach via rank reduction ⋮ On the geometric interpretation of the nonnegative rank ⋮ Polygons as sections of higher-dimensional polytopes ⋮ On the nonnegative rank of Euclidean distance matrices ⋮ Extension Complexity of Polytopes with Few Vertices or Facets ⋮ An upper bound for nonnegative rank ⋮ Common Information, Noise Stability, and Their Extensions

Cites Work

• Unnamed Item
• Nonnegative ranks, decompositions, and factorizations of nonnegative matrices
• A note on the computation of the CP-rank
• Semiring rank versus column rank
• Rank comparisons
• A comparison of nonnegative real ranks and their preservers

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