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PreprintCC BY 4.0arXiv

Split Quaternion Toolbox: A MATLAB Implementation

  • Salman Ahmadi-Asl
  • Abbas Moradi
  • Yang Zhang
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Abstract

This paper presents a MATLAB toolbox for working with split quaternions and split quaternion matrices. Split quaternions, also known as coquaternions, form a four-dimensional associative non-commutative algebra over the real numbers with a signature (+,+,-,-). The toolbox provides two main classes: SplitQuaternion for scalar-valued split quaternions and SplitQuaternionMatrix for matrix-valued split quaternions. The implementation includes arithmetic operations, algebraic functions, matrix operations, linear algebra utilities, and various conversion methods. The toolbox is designed to be intuitive for users familiar with MATLAB's standard matrix operations while providing the full power of split quaternion algebra. This paper details the implementation, provides numerous examples, and demonstrates the toolbox's capabilities through practical demonstrations. The MATLAB toolbox is accessible at https://github.com/SalmanAhmadi-Asl/Split_Quaternion.git.

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Cite

BibTeXRIS
BibTeX
@misc{ahmadiasl2026split,
  title = {{Split Quaternion Toolbox: A MATLAB Implementation}},
  author = {Salman Ahmadi-Asl and Abbas Moradi and Yang Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39904},
  eprint = {2610.39904},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39904},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Split Quaternion Toolbox: A MATLAB Implementation
AU  - Salman Ahmadi-Asl
AU  - Abbas Moradi
AU  - Yang Zhang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39904
UR  - https://arxiv.org/abs/2610.39904
AB  - This paper presents a MATLAB toolbox for working with split quaternions and split quaternion matrices. Split quaternions, also known as coquaternions, form a four-dimensional associative non-commutative algebra over the real numbers with a signature (+,+,-,-). The toolbox provides two main classes: SplitQuaternion for scalar-valued split quaternions and SplitQuaternionMatrix for matrix-valued split quaternions. The implementation includes arithmetic operations, algebraic functions, matrix operations, linear algebra utilities, and various conversion methods. The toolbox is designed to be intuitive for users familiar with MATLAB's standard matrix operations while providing the full power of split quaternion algebra. This paper details the implementation, provides numerous examples, and demonstrates the toolbox's capabilities through practical demonstrations. The MATLAB toolbox is accessible at https://github.com/SalmanAhmadi-Asl/Split_Quaternion.git.
ER  -