, Volume 20, Issue 2, pp 247-254
Date: 09 Jan 2010

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

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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.