$αβ$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra
Abstract
The \textit{-Tessarine Toolbox} is introduced as a high-performance MATLAB framework for generalized hypercomplex tensor algebra. By implementing the -tessarine mathematical structure, a strictly more general environment than existing quaternion or limited tessarine packages is provided. This open-source software bridges abstract theoretical models and experimental applications, allowing researchers to efficiently solve multidimensional problems. Built-in capabilities include exact hypercomplex matrix factorizations, such as Singular Value Decomposition (SVD) and QR, optimized for large-scale image in-painting, denoising, and digital watermarking. The scalable architecture facilitates new computational research in machine learning and multidimensional signal processing.
Cite
@article{arxiv.2607.27809,
title = {$αβ$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra},
author = {José Domingo Jiménez-López and Jesús Navarro-Moreno and Juan Carlos Ruiz-Molina},
journal= {arXiv preprint arXiv:2607.27809},
year = {2026}
}