In noncommutative algebra, a branch of mathematics, a quaternionic vector space is a module over the quaternions. Since the quaternion algebra is division ring, these modules are referred to as "vector spaces". However, the quaternion algebra is noncommutative.

Similar to vector spaces over a field. In this case we can use a standard basis which has the form

we use componentwise sum of vectors and product of vectors over scalars

we also use componentwise sum of vectors and product of vectors over scalars

See also

• Vector space

• General linear group

• Special linear group

• SL(n,H)

• Symplectic group

References