A pseudoscalar in a geometric algebra is a highest-grade element of the algebra.

The word problem here is thus to determine, given two such expressions, whether they represent the same element of the algebra.

The k-blades, because they are simple products of vectors, are called the simple elements of the algebra.

The exterior product extends to the full exterior algebra, so that it makes sense to multiply any two elements of the algebra.

In other words, the norm of an operator can be calculated using only the unitary elements of the algebra.

Not all the elements of the algebra are necessarily units.

The subalgebra plays role of the space of Fourier coefficients for elements of the algebra.

The relational algebra allows data duplication in the relations that are the elements of the algebra.

Here, and are elements of the geometric algebra, and is the spacetime vector derivative.

Although the algebra is created using real number scalars, the complex numbers and quaternions can still appear as other elements of the geometric algebra.