Difference between revisions of "Quaternion"
(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.) |
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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 | + | 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]]. |
==Operations== | ==Operations== | ||
| − | The quaternions obey all the usual arithmetic operations. Quaternions may be [[addition|added]], [[subtraction|subtracted]], and [[multiplication|multiplied]]. Addition is | + | 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. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 12:09, January 19, 2009
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-Latinate name "quaternion integer". Quaternions have proved useful in describing the mechanics of rotation.
Operations
The quaternions obey all the usual arithmetic operations. Quaternions may be added, subtracted, and 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.
