Advances in Applied Clifford Algebras

, Volume 20, Issue 2, pp 247-254

First online:

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

  • Henry Gillow-WilesAffiliated withDepartment of Science and Mathematics Education, Oregon State University
  • , Tevian DrayAffiliated withDepartment of Mathematics, Oregon State University Email author 

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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.


Octonions Hermitian matrices imaginary eigenvalues