Advances in Applied Clifford Algebras

, Volume 20, Issue 2, pp 247–254

Finding 3 × 3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues

Article

DOI: 10.1007/s00006-010-0201-4

Cite this article as:
Gillow-Wiles, H. & Dray, T. AACA (2010) 20: 247. doi:10.1007/s00006-010-0201-4
  • 47 Downloads

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.

Keywords.

OctonionsHermitian matricesimaginary eigenvalues

Copyright information

© Birkhäuser / Springer Basel AG, Switzerland 2010

Authors and Affiliations

  1. 1.Department of Science and Mathematics EducationOregon State UniversityCorvallisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA