The Set of Orthogonal Tensor Trains

2021/10/29 by Pardis Semnani, Semnani, Pardis, Elina Robeva +1
Mathematics · #14J11 (Primary) 1311 #14P05 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2110.15479

openalex publication_date 2021/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of orthogonally decomposable tensors is defined by appealing quadratic equations. The tensors we consider are an extension of orthogonally decomposable tensors. We show that they are defined by similar quadratic equations, as well as an interesting higher-degree additional equation.

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