Finding 3x3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues

Details Finding 3x3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues Finding 3x3 Hermitian Matrices over the Octonions with Imaginary Eigenvalues

2009-02-16

arxiv.org/abs/0902.2722v3

Mathematics

Rings and Algebras

9 pages, 1 figure; this version fixes typos only

Scientific paper

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.

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