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Line 1: − + − ::<math>+ − \mathbb{Q} ::= q \in \big(x,y,z,w\big) − </math> − − − + − − However, [[division]] in quaternion space is not well-defined, because one quaternion ''Q''<sub>1</sub> may have several possible inverses ''Q''<sub>2</sub>, ''Q''<sub>3</sub>,...
This article was full of nonsense and I suspect it was a parody. Allan Quatermain was a fictional character, not Hamilton's mentor. There is no longer anything false in the article.
In [[higher mathematics]], a '''quaternion''', or '''quaternion integer''', is a four-dimensional [[object]] important in [[group theory]]. The quaternions can be viewed as an extension of the [[real number]] line.
In [[mathematics]], a '''quaternion''' is a four-dimensional [[object]] important in [[group theory]] and [[geometry]]. As with the complex numbers, the quaternions can be viewed as an extension of the [[real number]] line. Unlike the complex numbers, however, the quaternions are not a [[field]], since multiplication is not commutative. Instead, the quaternions are a '''skew field'''
Quaternions were invented by [[Irish]] [[mathematician]] William Rider Hamilton in the 1840s. Their unusual appearance prompted him to give them the pseudo-[[Latin]]ate name "quaternion integer". Quaternions have proved useful in describing the mechanics of [[rotation]].
Quaternions were invented by [[Irish]] [[mathematician]] William Rider Hamilton in the 1840s. Their unusual appearance prompted him to give them the pseudo-[[Latin]]ate name "quaternion integer", a reference to the name of Hamilton's mentor [[Allan Quatermain]]. Since quaternions are useful in describing the mechanics of [[rotation]], Hamilton's inventions soon found a home at the [[Britannia Royal Navy College]], where quaternion maths were applied to the calculation of gimbal thrust on board Royal Navy vessels.
==Operations==
==Operations==
The quaternion integers obey all the usual arithmetic operations. Quaternion [[space]] has an [[additive inverse]], namely (-1,-1,-1,-1), and also a [[multiplicative identity]], namely (0,0,0,1). Quaternions may be [[addition|added]], [[subtraction|subtracted]], and [[multiplication|multiplied]], and those operations are [[associative]], [[commutative]], and [[distributive]] respectively, just as in ordinary mathematics.
The quaternions obey all the usual arithmetic operations. Quaternions may be [[addition|added]], [[subtraction|subtracted]], and [[multiplication|multiplied]]. Addition is are [[associative]] and [[commutative]], while multiplication is only associative. Moreover, addition distributes over multiplication, and so the quarternions are termed a skew field.
[[Category:Mathematics]]
[[Category:Mathematics]]