Quaternionic vector space
In mathematics, a left (or right) quaternionic vector space is a left (or right) H-module where H is the (non-commutative) division ring of quaternions. The space H of "n"-tuples of quaternions is both a left and right H-module using the componentwise left and right multiplication: for quaternions "q" and "q", "q", ... "q". Since H is a division algebra, every finitely generated (left or right) H-module has a basis, and hence is isomorphic to H for some "n".