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$αβ$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra

Commutative Algebra 2026-07-30 v1 Dynamical Systems Spectral Theory

Abstract

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

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}
}