Minimality of tensors of fixed multilinear rank
Differential Geometry
2021-12-14 v3 Algebraic Geometry
Abstract
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of fixed multilinear rank form a minimal submanifold of the Euclidean space of tensors endowed with the Frobenius inner product. We also establish the absence of local extrema for linear functionals restricted to the submanifold of rank-one tensors, finding application in statistics.
Keywords
Cite
@article{arxiv.2007.08909,
title = {Minimality of tensors of fixed multilinear rank},
author = {Alexander Heaton and Khazhgali Kozhasov and Lorenzo Venturello},
journal= {arXiv preprint arXiv:2007.08909},
year = {2021}
}
Comments
12 pages, 1 figure