  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.
