Quaternion Toolbox for Matlab (QTFM). Matlab® is a proprietary software system for calculating with matrices of real and complex numbers, developed and sold by The MathWorks. Quaternions are hypercomplex numbers (that is generalizations of the complex numbers to higher dimensions than two). For an introduction, refer to the Wikipedia article on Quaternions. For an introduction to octonions, refer to the Wikipedia article: Octonions. Quaternion toolbox for Matlab® extends Matlab® to allow calculation with matrices of quaternions in almost the same way that one calculates with matrices of complex numbers. This is achieved by defining a private type to represent quaternion matrices and overloadings of many standard Matlab® functions. The toolbox supports real and complex quaternions (that is quaternions with four real or complex components). From version 2 of the toolbox, octonions are also supported (but not to the same extent, or with the same level of maturity as the quaternions).

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Błaszczyk, Łukasz: Discrete octonion Fourier transform and the analysis of discrete 3-D data (2020)
  2. Ma, Ru-Ru; Bai, Zheng-Jian: A structure-preserving one-sided Jacobi method for computing the SVD of a quaternion matrix (2020)
  3. Sangwine, Stephen J.; Hitzer, Eckhard: Polar decomposition of complexified quaternions and octonions (2020)
  4. Fletcher, Peter: Discrete wavelets with quaternion and Clifford coefficients (2018)
  5. Hitzer, Eckhard: General two-sided quaternion Fourier transform, convolution and mustard convolution (2017)
  6. Hitzer, Eckhard: Quaternionic Wiener-Khinchine theorems and spectral representation of convolution with steerable two-sided quaternion Fourier transform (2017)
  7. Ling, Si-Tao; Jia, Zhi-Gang; Jiang, Tong-Song: LSQR algorithm with structured preconditioner for the least squares problem in quaternionic quantum theory (2017)
  8. Li, Ying; Wei, Musheng; Zhang, Fengxia; Zhao, Jianli: A real structure-preserving method for the quaternion LU decomposition, revisited (2017)
  9. Sangwine, Stephen J.; Hitzer, Eckhard: Clifford multivector toolbox (for MATLAB) (2017)
  10. Li, Ying; Wei, Musheng; Zhang, Fengxia; Zhao, Jianli: Real structure-preserving algorithms of Householder based transformations for quaternion matrices (2016)
  11. Grigoryan, Artyom M.; Agaian, Sos S.: Tensor transform-based quaternion Fourier transform algorithm (2015)
  12. Li, Ying; Wei, Musheng; Zhang, Fengxia; Zhao, Jianli: A fast structure-preserving method for computing the singular value decomposition of quaternion matrices (2014)
  13. Wang, Minghui; Ma, Wenhao: A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory (2013)
  14. Sangwine, Stephen J.; Ell, Todd A.: Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler’s formula (2012)
  15. Guo, Li-Qiang; Zhu, Ming: Quaternion Fourier-Mellin moments for color images (2011)
  16. Sangwine, Stephen J.; Ell, Todd A.; Le Bihan, Nicolas: Fundamental representations and algebraic properties of biquaternions or complexified quaternions (2011)
  17. Took, Clive Cheong; Mandic, Danilo P.: Augmented second-order statistics of quaternion random signals (2011)
  18. Wang, Minghui: Algorithm Q-LSQR for the least squares problem in quaternionic quantum theory (2010)
  19. Le Bihan, Nicolas; Sangwine, Stephen J.: Jacobi method for quaternion matrix singular value decomposition (2007)
  20. Sangwine, Stephen J.; Le Bihan, Nicolas: Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations (2006)