Difference between revisions of "Quaternion"
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Latest revision as of 11:29, 27 September 2024
The quaternions are a division ring (that is, a ring in which each element has a multiplicative inverse; alternatively, a noncommutative field) which generalize the complex numbers.
Formally, the quaternions are the set 
, where 
are any real numbers and the behavior of 
is "as you would expect," with the properties:
, 
and 
, 
and 
Note in particular that multiplication of quaternions is not commutative. However, multiplication on certain subsets does behave well: the set 
act exactly like the complex numbers.
See Also
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