Finding 3x3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues

Abstract

We show that any 3-component octonionic vector which is purely imaginary, but not quaternionic, is an eigenvector of a 6-parameter family of Hermitian octonionic matrices, with imaginary eigenvalue equal to the associator of its elements.

9 pages, 1 figure; this version fixes typos only