Quaternion

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-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 are associative and commutative, while multiplication is only associative. Moreover, addition distributes over multiplication, and so the quarternions are termed a skew field.