Conventions – Geometric Algebra

As GA is still in evolution, people around the world hasn’t settled down to a common way of indicating elements and operations. Here are the ones that we believe are the most common and least likely to cause confusion.

Symbol	Meaning
$e_1, e_2 ... e_k$	orthonormal basis vectors
$\pmb{v}, \pmb{w} ...$	vector (bold lowercase letter)
$B, D ...$	bivector
$I$	unit pseudoscalar
$M^{-1}$	inverse of a multivector M (in eucledian space $M^{-1} = M^\dagger$ )
$M^\dagger$	conjugate (reverse) of a multivector M; it is also indicated with tilde above $\widetilde{M}$ , especially in spacetime algebra
$M^*$	dual of a multivector, i.e. its representation in the orthogonal complement
$R = e^{-B\frac{\theta}{2}}$	rotor of amplitude $\theta$ on B plane (bivector) coherent with the orientation of B
$R = e^{-i\pmb{n}\frac{\theta}{2}}$	rotor of amplitude $\theta$ around the $\pmb{n}$ axis (3D only)
$M \mapsto RMR^{-1}$	generalized rotation of multivector M by the rotor R

Leave a Reply Cancel reply