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arXiv · 2607.27809

$\alpha\beta$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra

José Domingo Jiménez-López·Jesús Navarro-Moreno·Juan Carlos Ruiz-Molina
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Abstract

The \textit{$\alpha\beta$-Tessarine Toolbox} is introduced as a high-performance MATLAB framework for generalized hypercomplex tensor algebra. By implementing the $\alpha\beta$-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.

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José Domingo Jiménez-López, Jesús Navarro-Moreno, Juan Carlos Ruiz-Molina. 2026-07-30. $\alpha\beta$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra. https://arxiv.org/abs/2607.27809

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