Implementation Details

Blade Representation

In GeometricAlgebra.jl, blades are represented using a multiplicative representation where each blade is stored as

• a matrix containing an orthonormal basis for the subspace represented by the blade and

• a scalar value representing the magnitude and orientation of the blade.

For numerical computing, this representation has the following advantages.

• A blade's dimension $n$ and grade $k$ are limited by only the availability of RAM to store $n \times k$ matrices.

• State-of-the-art numerical linear algebra algorithms can be leveraged to implement geometric algebra operations.

For more details, see Fontijne's PhD Thesis in the References.