Quaternion

Four-dimensional number system extending the complex numbers — commutativity of multiplication is the first property the tower gives up.

Specifications & Metrics

type

Cayley–Dickson Algebras

originator

William Rowan Hamilton

introduced

1843

symbol

a + bi + cj + dk

Core Principles & Analysis

• A number system with four real-number components instead of the complex numbers' two, usually written a + bi + cj + dk.
• Quaternion multiplication is not commutative: the result depends on the order of the factors.
• Hamilton discovered them in 1843 and carved the defining formula into the stone of Brougham Bridge with his pocket knife.

Sources

• Wikipedia: Quaternion