Quaternionic vector space
In mathematics, a left quaternionic vector space is a left H-module where H denotes the noncommutative ring of the quaternions.
The space Hn of n-tuples of quaternions is both a left and right H-module using the componentwise left and right multiplication:
for quaternions q and q1, q2,... qn.
Since H is a division algebra, every finitely generated H-module has a basis, and hence is isomorphic to Hn for some n.
