On 14/10/2020 01:33, Dan Asimov wrote:
Henry,
Despite whatever else you say, you also said:
----- We have thus factored our quaternion into two complex numbers sqrt(AB) and 1/sqrt(A'B), and a quaternion having only real (rather than complex) components. ----- ... So maybe that's not what you mean, or maybe you don't mean that you have factored a quaternion into two complex numbers.
Surely what it actually says is that a quaternion has been written as a product of _three_ things: - a "complex number" (only 1,i) - another "complex number" (only 1,i) - a "quaternion having only real components" (only 1,j). Which is not at all the same thing as claiming to have factored a quaternion into two complex numbers. (Your earlier email seems to imply that even this weaker claim is known to be impossible, which seems surprising to me; but I might have misunderstood, or there might be a surprising theorem; both have happened before.) -- g