Quaternion
Numbers with four dimensions are called quaternions. You write them as
x = x0 e0 + x1 e1 + x2 e2 + x3 e3
and consists of the real numbers xa and the units
{ e0 , e1 , e2 , e3 }
The unit e0 is the real number 1.
Explanation
When multiplying the units { e0 , e1 , e2 , e3 } the order plays a role.
× e0 e1 e2 e0 e0 e1 e2 e1 e1 −e0 e3 e2 e2 −e3 −e0
Quaternions can therefore be used to describe a rotation in three dimensions. A point (x1, x2, x3) in three dimensions forms the imaginary part x1e1, x2e2, x3e3 of a quaternion.
HistoryThis notation was proposed in 1844 by the German mathematician Hermann Grassmann, who developed linear algebra. |