Quaternion

From Conservapedia

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.

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", 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

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 added, subtracted, and multiplied, and those operations are associative, commutative, and distributive respectively, just as in ordinary mathematics.

However, division in quaternion space is not well-defined, because one quaternion Q₁ may have several possible inverses Q₂, Q₃,...