New lower bounds on tensor rank of $(2,n,m)$ matrix multiplication with GPT-6

2026-09-13

AI Summary

该研究使用GPT-6为(2,n,m)矩阵乘法的张量秩设定了新的下界，解决了特定条件下张量秩最小值的问题。

Abstract

The tensor rank of $2\times n$-with-$n\times m$ matrix multiplication is at least $(n+2)m$ if $n\ge 4$ and at least $\left\lceil \frac{24}{5}m \right\rceil$ if $n=3$. Both lower bounds apply over arbitrary fields.

Problem

• tensor rank
• matrix multiplication
• lower bounds

Innovation

• tensor rank
• matrix multiplication
• lower bounds