Intrinsic Construction of the Algebra of Quaternions

摘要

A construction of the algebra of quaternions from first principles of real linearalgebra while using specific vector space bases as little as possible is presented. The theory of quaternions is developed from the departure point of general elementary theory of groups, finite dimensional real inner product spaces, and algebras. A coordinate independent development in two main steps, namely a coordinate independent definition of the outer product in three dimensional real vector space, and a definition of the quaternions, using the inner and outer product in three dimensional vector space is given.