Quaternionic vector space

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. 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.

See also

• Vector space
• General linear group
• Special linear group
• SL(n,H)
• Symplectic group

References

• Harvey, F. Reese (1990). Spinors and Calibrations. San Diego: Academic Press. ISBN 0-12-329650-1.