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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'''

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 Rowan 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 Rowan Hamilton in the 1840s. Quaternions have proved useful in describing the mechanics of [[rotation]].

==Operations==

==Operations==

The quaternions obey all the usual arithmetic operations. Quaternions may be [[addition|added]], [[subtraction|subtracted]], and [[multiplication|multiplied]].  Addition is [[associative]] and [[commutative]], while multiplication is only associative.  Moreover, addition distributes over multiplication, and so the quarternions are termed a skew field.

The quaternions obey all the usual arithmetic operations. Quaternions may be [[addition|added]], [[subtraction|subtracted]], [[multiplication|multiplied]], and [[division|divided]].  Addition is [[associative]] and [[commutative]], while multiplication is only associative.  Moreover, addition distributes over multiplication and nonzero quaternions have multiplicative inverses, and so the quarternions are termed a skew field.

[[Category:Mathematics]]

[[Category:Mathematics]]