Quaternion and octonion toolbox for Matlab®

September 2015: QTFM release 2.2 marks the second decade of this open-source toolbox, which was first released on 3 August 2005. In ten years the toolbox has been downloaded over 13,000 times.

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).


The toolbox is licensed under the GNU General Public License.


Versions of the toolbox up to 1.9 require MATLAB® Version 7.4 (R2007a) or later. Version 2 of the toolbox requires MATLAB® Version 7.14 (R2012a) or later.

How to get the toolbox

To access the latest release and CVS repository or to email the authors, follow this link to the project summary page. We make releases at irregular intervals, but update individual files in the CVS repository. To be fully up-to-date you should download the latest release, and then any files that have changed since the release date. Access to the CVS repository is possible through a web interface that makes it easy to download individual files.

Mailing list

To receive announcements about new releases of the toolbox, significant updates etc, please subscribe to the QTFM-announce mailing list.

The toolbox was developed by Steve Sangwine and Nicolas Le Bihan at the Département Images et Signal, GIPSA-Lab in Grenoble, France. (Steve Sangwine is based at the University of Essex, United Kingdom, but spent 7 months in Grenoble as a Visiting Researcher in 2005.)
Created: 27 July 2005. Updated: 30 September 2015.
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