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Type: Journal article
Title: The vector algebra war: a historical perspective
Author: Chappell, J.
Iqbal, A.
Hartnett, J.
Abbott, D.
Citation: IEEE Access, 2016; 4:1997-2004
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Issue Date: 2016
ISSN: 2169-3536
Statement of
James M. Chappell, Azhar Iqbal, John G. Hartnett, and Derek Abbott
Abstract: There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs’ three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, and quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of 19th century science was to suitably describe vectors in 3-D space. This situation also has the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford’s multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.
Keywords: Vectors; Gibbs; Hamilton; Clifford; multivectors
Description: Date of Publication : 11 March 2016
Rights: © 2016 IEEE.
RMID: 0030047875
DOI: 10.1109/ACCESS.2016.2538262
Appears in Collections:Electrical and Electronic Engineering publications

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