complex plane equipollent quaternions W.R. Hamilton hypercomplex number basis
Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in 




C



{\displaystyle \mathbb {C} }

 have a difference w – z, and the line segments wz and 0(w − z) are of the same length and direction. The segments are equipollent. The four-dimensional system 




H



{\displaystyle \mathbb {H} }

 of quaternions was discovered by W.R. Hamilton in 1843.  The term vector was introduced as v = xi + yj + zk representing a point in space. The quaternion difference p – q also produces a segment equipollent to pq. Other hypercomplex number systems also used the idea of a linear space with a basis.
