Difference between revisions of "Quaternion"
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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 | + | 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. 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]]. | ||
Revision as of 15:40, February 8, 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. Quaternions have proved useful in describing the mechanics of rotation.
Operations
The quaternions obey all the usual arithmetic operations. Quaternions may be added, subtracted, multiplied, and 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.