Linear functions Although a versor is easier to work with because it can be directly represented in the algebra as a multivector, versors are a subgroup of linear functions on multivectors, which can still be used when necessary. The geometric algebra of an -dimensional vector space is spanned by a basis of elements. If a multivector is represented by a real column matrix of coefficients of a basis of the algebra, then all linear transformations of the multivector can be expressed as the matrix multiplication by a real matrix. However, such a general linear transformation allows arbitrary exchanges among grades, such as a "rotation" of a scalar into a vector, which has no evident geometric interpretation.
linear functions although a versor is easier to work with because it can be directly represented in the algebra as a multivector versors are a subgroup of linear functions on multivectors which can still be used when necessary the geometric algebra of an -dimensional vector space is spanned by a basis of elements if a multivector is represented by a real column matrix of coefficients of a basis of the algebra then all linear transformations of the multivector can be expressed as the matrix multiplication by a real matrix however such a general linear transformation allows arbitrary exchanges among grades such as a "rotation" of a scalar into a vector which has no evident geometric interpretation