Talk:Frobenius theorem (real division algebras)
|WikiProject Mathematics||(Rated Stub-class, Low-importance)|
Is it possible someone would be able to include a proof for this?
Serious mistake in proof
If is orthonormal basis, then by definition of orthonormality, so the claim is wrong (actually not completely wrong, but doesn't make any sense since ) and the following arguments about quaternions and case n>2 are also wrong.
Also there's a type in case n=2: , it should be for the case of quaternions, but it would contradict with orthogonality. — Preceding unsigned comment added by 18.104.22.168 (talk) 11:03, 3 October 2012 (UTC)
There is no mistake: Orthonormality says that the inner product is zero, not that the algebra product is zero. The definition of the inner product is . Thus . Mike Stone (talk) 15:32, 11 June 2013 (UTC)