Upper bound of typical ranks of m x n x ((m-1)n-1) tensors over the real number field

2013/04/26 by Toshio Sumi, Sumi, Toshio, Toshio Sakata +3
Computer Science · Mathematics · #Algorithms and Data Compression #FOS: Mathematics #Mathematical Approximation and Integration #Rings and Algebras (math.RA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1304.7260

openalex publication_date 2013/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 3≤ m≤ n. We study typical ranks of m× n× ((m-1)n-1) tensors over the real number field. The number (m-1)n-1 is a minimal typical rank of m× n× ((m-1)n-1) tensors over the real number field. We show that a typical rank of m× n× ((m-1)n-1) tensors over the real number field is less than or equal to (m-1)n and in particular, m× n× ((m-1)n-1) tensors over the real number field has two typical ranks (m-1)n-1, (m-1)n if m≤ ρ(n), where ρ is the Hurwitz-Radon function defined as ρ(n)=2^b+8c for nonnegative integers a,b,c such that n=(2a+1)2^b+4c and 0≤ b<4.

Citations

• Tensor Decompositions and Applications

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