Classifying Octonionic-Linear Operators

June 2017The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis of linear operators that maps to the canonical basis of matrices for each space. Finally, we discuss automorphisms of the octonions, a special subset of the linear operators