Clifford Multivector Toolbox

A toolbox for computing with Clifford algebras in Matlab

MatlabŪ is a proprietary software system for calculating with matrices of real and complex numbers, developed and sold by The MathWorks.

The Clifford algebras are a family of hypercomplex algebras, each element of which is known as a multivector. For an introduction, refer to the Wikipedia articles on Clifford algebra and Multivector.

The Clifford multivector toolbox for MatlabŪ extends MatlabŪ to allow calculation with matrices of multivectors in almost the same way that one calculates with matrices of complex numbers. This is achieved by defining a private type to represent multivector matrices and overloadings of many standard MatlabŪ functions. The toolbox supports multivectors with real or complex elements in any numeric data type supported by Matlab.


The toolbox is licensed under the GNU General Public License.


We recommend a recent version of Matlab (R2014 onwards), as the toolbox has not been tested with older versions.

How to get the toolbox

To access the latest release and SVN repository or to email the authors, follow this link to the project summary page or click this logo Download Clifford Multivector Toolbox.

We make releases at irregular intervals, but update individual files in the SVN 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 SVN 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 Clifford-multivector-toolbox mailing list.

The toolbox was developed by Steve Sangwine and Eckhard Hitzer.
Created: 22 June 2015.
Download Clifford Multivector Toolbox