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Research Article | Open Access

Some insights into rank conditions of vector subspaces

Zoran Z. Petrović1, Zoran S. Pucanović2( ), Marko D. Pešović2, Miloš A. Kovačević2
Faculty of Mathematics, University of Belgrade, Studentski trg 16, Belgrade, Serbia
Faculty of Civil Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, Serbia
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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.

Keywords

rank functionsubspaces with rank conditionstensor decompositionstensor rank
CLC number: 15A03, 15A69, 15A72

References

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 23711-23723
DOI: 10.3934/math.20241152

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Cite this article:
Petrović ZZ, Pucanović ZS, Pešović MD, et al. Some insights into rank conditions of vector subspaces. AIMS Mathematics, 2024, 9(9): 23711-23723. https://doi.org/10.3934/math.20241152

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Received: 09 June 2024
Revised: 24 July 2024
Accepted: 30 July 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)