@article{Petrović2024, 
author = {Zoran Z. Petrović and Zoran S. Pucanović and Marko D. Pešović and Miloš A. Kovačević},
title = {Some insights into rank conditions of vector subspaces},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {23711-23723},
keywords = {rank function, subspaces with rank conditions, tensor decompositions, tensor rank},
url = {https://www.sciopen.com/article/10.3934/math.20241152},
doi = {10.3934/math.20241152},
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.}
}