6 papers
Orthonormal Eigenbases over the Octonions
Tevian Dray, Corinne A Manogue, Susumu Okubo
We previously showed that the real eigenvalues of 3x3 octonionic Hermitian matrices form two separate families, each containing 3 eigenvalues, and each leading to an orthonormal de…
Some Properties of 3x3 Octonionic Hermitian Matrices with Non-Real Eigenvalues
Tevian Dray, Jason Janesky, Corinne A. Manogue
We discuss our preliminary attempts to extend previous work on 2x2 Hermitian octonionic matrices with non-real eigenvalues to the 3x3 case.
Octonionic Hermitian Matrices with Non-Real Eigenvalues
Tevian Dray, Jason Janesky, Corinne A. Manogue
We extend previous work on the eigenvalue problem for Hermitian octonionic matrices by discussing the case where the eigenvalues are not real, giving a complete treatment of the 2x…
The Exceptional Jordan Eigenvalue Problem
Tevian Dray, Corinne A. Manogue
We discuss the eigenvalue problem for 3x3 octonionic Hermitian matrices which is relevant to the Jordan formulation of quantum mechanics. In contrast to the eigenvalue problems con…
Quaternionic Spin
Tevian Dray, Corinne A. Manogue
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equ…
The Octonionic Eigenvalue Problem
Tevian Dray, Corinne A. Manogue
We discuss the eigenvalue problem for 2x2 and 3x3 octonionic Hermitian matrices. In both cases, we give the general solution for real eigenvalues, and we show there are also soluti…