Minimality of tensors of fixed multilinear rank

Alexander Heaton; Khazhgali Kozhasov; Lorenzo Venturello

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Minimality of tensors of fixed multilinear rank

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arxiv 2007.08909 v3 pith:VUBC4IP7 submitted 2020-07-17 math.DG math.AG

Alexander Heaton , Khazhgali Kozhasov , Lorenzo Venturello This is my paper · ORCID

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keywords tensorsfixedmultilinearrankspacesubmanifoldabsenceapplication

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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.

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