An Axiomatic Approach to Tensor Rank Functions
Functional Analysis
2020-12-10 v1 Rings and Algebras
Abstract
Recent work of Qi et al. arXiv:2004.11240v7 proposes a set of axioms for tensor rank functions. The current paper presents examples showing that their axioms allow rank functions to have some undesirable properties, and a stronger set of axioms is suggested that eliminates these properties. Two questions raised by Qi et al. involving the submax rank function are also answered.
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Cite
@article{arxiv.2012.04730,
title = {An Axiomatic Approach to Tensor Rank Functions},
author = {Wayne W. Wheeler},
journal= {arXiv preprint arXiv:2012.04730},
year = {2020}
}
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11 pages