Clifford Algebra

Abstract

At the turn on the nineteenth century there was a vituperative dispute about which was the ‘correct’ notation to use in modern geometry. The matrix-vector methods promoted by Gibbs won and the quaternion-Clifford algebra methods lost. This is why modern students in science and engineering no longer learn about quaternions. However, news of this revolution was slow to spread in some areas, particularly in kinematics. So Study and latter Blaschke [12] and Dimentberg [27] continued to develop ‘dual quaternions’ and applied them to the theory of mechanisms. Mathematicians never really forgot about these things, although the real impetus to look at these structures afresh came when physicists rediscovered them. Pauli’s σ-matrices and Dirac’s γ-matrices turned out to be generators of Clifford algebras.