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AIMS Mathematics

2024, Volume 9, Issue 9: 23711-23723. doi: 10.3934/math.20241152
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Research article

Some insights into rank conditions of vector subspaces

  • 1.
    Faculty of Mathematics, University of Belgrade, Studentski trg 16, Belgrade, Serbia
  • 2.
    Faculty of Civil Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, Serbia
  • Received: 09 June 2024 Revised: 24 July 2024 Accepted: 30 July 2024 Published: 08 August 2024

  • MSC : 15A03, 15A69, 15A72

  • 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.

    Citation: Zoran Z. Petrović, Zoran S. Pucanović, Marko D. Pešović, Miloš A. Kovačević. Some insights into rank conditions of vector subspaces[J]. AIMS Mathematics, 2024, 9(9): 23711-23723. doi: 10.3934/math.20241152

    Related Papers:

  • 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.



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