标题： 八元数上的规范正交特征基 显示英文标题

标题： Orthonormal Eigenbases over the Octonions

摘要： 我们之前证明了3×3八元数Hermite矩阵的实特征值形成两个不同的族，每族包含3个特征值，并且每个族都可导致单位矩阵的规范正交分解，这通常对应于规范正交基。我们在这里表明，尽管如此，为了将一个任意向量分解为原始矩阵的特征向量的分量，仍需要这两个族；因此，每个向量有6个分量，而不是3个。 显示英文摘要

摘要： 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.