Publications
Article · Linear and Multilinear Algebra · April 19, 2022
Minimality of tensors of fixed multilinear rank
Alexander Heaton, Khazhgali Kozhasov, Lorenzo Venturello
Abstract
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of the 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.
Tensor decomposition and applicationsAdvanced Combinatorial MathematicsAdvanced Differential Geometry Researchmultilinear rankminimal submanifoldsrank-one tensors
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