Orthonormal Eigenbases over the Octonions

Details Orthonormal Eigenbases over the Octonions Orthonormal Eigenbases over the Octonions

2001-06-04

arxiv.org/abs/math/0106021v1

Mathematics

Rings and Algebras

LaTeX2e, 14 pages

Scientific paper

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 decomposition of the identity matrix, which would normally correspond to an orthonormal basis. We show here that it nevertheless takes both families in order to decompose an arbitrary vector into components, each of which is an eigenvector of the original matrix; each vector therefore has 6 components, rather than 3.

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