Euclidean Vector - History

History

The concept of vector, as we know it today, evolved gradually over a period of more than 200 years. About a dozen people made significant contributions. The immediate predecessor of vectors were quaternions, devised by William Rowan Hamilton in 1843 as a generalization of complex numbers. His search was for a formalism to enable the analysis of three-dimensional space in the same way that complex numbers had enabled analysis of two-dimensional space. In 1846 Hamilton divided his quaternions into the sum of real and imaginary parts that he respectively called "scalar" and "vector":

The algebraically imaginary part, being geometrically constructed by a straight line, or radius vector, which has, in general, for each determined quaternion, a determined length and determined direction in space, may be called the vector part, or simply the vector of the quaternion. —W. R. Hamilton, London, Edinburgh & Dublin Philososphical Magazine 3rd series 29 27 (1846)

Whereas complex numbers have one number whose square is negative one, quaternions have three independent such numbers . Multiplication of these numbers by each other is not commutative, e.g., . Multiplication of two quaternions yields a third quaternion whose scalar part is the negative of the modern dot product and whose vector part is the modern cross product.

Peter Guthrie Tait carried the quaternion standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator and is very close to modern vector analysis.

Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwell's Treatise on Electricity and Magnetism, separated off their vector part for independent treatment. The first half of Gibbs's Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis.