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Bounds on strongly orthogonal ranks of tensors

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  • Hu, Shenglong

Abstract

A strongly orthogonal decomposition of a tensor is a rank-one tensor decomposition with the two component vectors in each mode of any two rank-one tensors are either colinear or orthogonal. A strongly orthogonal decomposition with the smallest possible number of rank-one tensors is a strongly orthogonal rank decomposition. Any tensor has a strongly orthogonal rank decomposition. The number of rank-one tensors in a strongly orthogonal rank decomposition is the strongly orthogonal rank. In this article, bounds on the strongly orthogonal rank of a real tensor are investigated. A universal upper bound, in terms of the multilinear ranks, for the strongly orthogonal ranks is given for an arbitrary tensor space. A formula for the expected strongly orthogonal rank of a given tensor space is also given, which is verified for a set of tensor spaces numerically.

Suggested Citation

  • Hu, Shenglong, 2020. "Bounds on strongly orthogonal ranks of tensors," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    • Handle: RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319307155
    DOI: 10.1016/j.amc.2019.124723
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