# Tensor-Tensor Product Toolbox

arXiv: https://arxiv.org/abs/1806.07247 · HTML: https://mlsanity.com/paper/1806.07247/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2018.

## Built on by (most cited first, 4 of 4)

- [Efficiency of First-Order Methods for Low-Rank Tensor Recovery with the Tensor Nuclear Norm Under Strict Complementarity](https://mlsanity.com/paper/2308.01677/) (2023)
- [Power of ℓ1-Norm Regularized Kaczmarz Algorithms for High-Order Tensor Recovery](https://mlsanity.com/paper/2405.08275/) (2024)
- [Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems](https://mlsanity.com/paper/2503.18190/) (2025)
- [Tensor Dynamic Mode Decomposition](https://mlsanity.com/paper/2508.02627/) (2025)

## Abstract (arXiv)

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor spectral norm, tensor nuclear norm [C. Lu, et al., 2018] and many others. The linear algebraic structure of tensors are similar to the matrix cases. We develop a Matlab toolbox to implement several basic operations on tensors based on t-product. The toolbox is available at https://github.com/canyilu/tproduct.