Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/1697
Title: Some insights into rank conditions of vector subspaces
Authors: Petrović, Zoran 
Pucanović, Zoran S.
Pešović, Marko D.
Kovačević, Miloš A.
Affiliations: Algebra and Mathematical Logic 
Keywords: rank function;subspaces with rank conditions;tensor decompositions;tensor rank
Issue Date: 1-Jan-2024
Rank: M21a
Publisher: AIMS press
Journal: AIMS Mathematics
Abstract: 
We introduce the general notion of a rank on a vector space, which includes both tensor rank and conventional matrix rank, but incorporates other examples as well. Extending this concept, we investigate vector spaces consisting of vectors with a lower bound on their rank. Our main result shows that bases for such spaces of maximum dimension can be chosen to consist exclusively of vectors of minimal rank. This generalization extends the results of [15, 36], with potential applications in different areas.
URI: https://research.matf.bg.ac.rs/handle/123456789/1697
DOI: 10.3934/math.20241152
Appears in Collections:Research outputs

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