A counterexample to Strassen's direct sum conjecture

2017/12/22 by Yaroslav Shitov, Shitov, Yaroslav · 3 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Tensor decomposition and applications #math.CO

paper · pdf · doi:10.48550/arxiv.1712.08660

10 pages

arxiv created 2017/12/22 · openalex publication_date 2017/12/22 · arxiv updated 2017/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The rank of tensors is not additive with respect to the direct sum.

Cited by

• Detecting Direct Sums of Tensors and Their Limits
• On the construction of a counterexample to Strassen's rank additivity conjecture
• Unifying singular value decompositions of tensors via aligned orthogonality

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