Orthonormal Eigenbases over the Octonions
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:math/0106021
 Bibcode:
 2001math......6021D
 Keywords:

 Rings and Algebras;
 15A33;
 15A18;
 17A35;
 17C99
 EPrint:
 LaTeX2e, 14 pages