In mathematics, a left (or right) quaternionic vector space is a left (or right) 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 (left or right) H-module has a basis, and hence is isomorphic to Hn for some n.
- Harvey, F. Reese (1990). Spinors and Calibrations. San Diego: Academic Press. ISBN 0-12-329650-1.