Quaternionic vector space
- 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 H"n" 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"1, "q"2, ... "q""n".
Since H is a division algebra, every finitely generated (left or right) H-module has a basis, and hence is isomorphic to H"n" for some "n".
ee also
* Vector space
* General linear group
* Special linear group
* SL(n,H)
* Symplectic group
References
*cite book
first = F. Reese
last = Harvey
year = 1990
title = Spinors and Calibrations
publisher = Academic Press
location = San Diego
id = ISBN 0-12-329650-1
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