Open AccessA linear associative algebra suitable for electromagnetic relations and the theory of relativity
Author(s) -
W. J. Johnston
Publication year - 1919
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1919.0060
Subject(s) - clifford algebra , minkowski space , associative property , algebra over a field , simple (philosophy) , mathematics , unit (ring theory) , pure mathematics , theory of relativity , physics , theoretical physics , mathematical physics , mathematics education , philosophy , epistemology
Clifford has pointed out that geometrical algebras may be based on a system of fundamental units,i, j, k, o , etc., these units being alternate (ij = —ji ,io = —oi , etc.), and the square of each unit being —1. It can beproved that such a system is associative. Such an algebra based on four fundamental units,i, j, k, o , expresses in a remarkably simple manner the vector formulæ of Minkowski and the electromagnetic relations.