Quaternion, a non-commutative extension of the complex numbers
Quaternion math may also be used but that is outside the scope of this article.
The Toolbox provides functions for manipulating and converting between datatypes such as: vectors;homogeneous transformations; roll-pitch-yaw and Euler angles and unit-quaternions which are necessary to represent 3-dimensional position and orientation.
Quaternion | quaternion | "Quaternion Eagle", '''Coat of arms of the Holy Roman Empire | Hyperbolic quaternion |
Around this time Josiah Willard Gibbs and Oliver Heaviside developed vector calculus, which included separate cross product and dot products that were derived from quaternion multiplication.
Oliver Heaviside in England and Josiah Willard Gibbs, a professor at Yale University in Connecticut, also felt that quaternion methods were too cumbersome, often requiring the scalar or vector part of a result to be extracted.
The book by Hervé Jacquet and Langlands on presented a theory of automorphic forms for the general linear group , establishing among other things the Jacquet–Langlands correspondence showing that functoriality was capable of explaining very precisely how automorphic forms for related to those for quaternion algebras.
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This book applied the adelic trace formula for and quaternion algebras to do this.
In 1843, while walking with his wife along the Royal Canal, Sir William Rowan Hamilton realised the formula for quaternions and carved his initial thoughts into a stone on the Brougham Bridge over the canal.
Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis.