Subject: Re: Algebraic equations in quaternions
Date: Tue, 3 Mar 1998 11:08:30 -0500
From: Alex Bogomolny
Thank you for the kind words.
In the algebra of quaternions, the equation x2 + 1 = 0 has infinitely many solutions, not just 6: any x = ai + bj, where a2 + b2 = 1, satisfies the equation. So I would assume that the theory of algebraic equations on such an algebra is not very interesting.
I think the situation is analogous to the matrix algebra. Every square matrix satisfies its characteristic equation. But there are infinitely many matrices that share exactly same characteristic equation.