Talk:Field Norm of Quaternion is not Norm

The field norm of Quaternion does not satisfy the :
 * $n(1 + 1) = 4 > 2 = n(1) + n(1)$

The square root of $n$ is a norm, and in some sources this is known as the Quaternion norm.

I’m not sure how the field norm of Quaternion should be classified.

Mathworld has an interesting take on a generalisation of the norm called a valuation, but this is not the same definition as the valuation on.

—Leigh.Samphier (talk) 07:20, 26 April 2019 (EDT)


 * Heh. Yes, we have the same problem with this as we did with the complex number norm. I'll look at this in due course. --prime mover (talk) 08:33, 26 April 2019 (EDT)


 * There. Anything else that may need to be adjusted and / or corrected can be done in the context of this, now. --prime mover (talk) 14:55, 26 April 2019 (EDT)


 * So we can now introduce $\sqrt{\mathbf x \overline {\mathbf x}}$ as a norm on the quaternions. The question is what to call it. Various sources call it either the Norm or the Modulus. Most online sources refer to it as the Norm (Mathworld, PlanetMath, and, dare I say, WikiPedia). Sources that call $\mathbf x \overline {\mathbf x}$ the norm, call $\sqrt{\mathbf x \overline {\mathbf x} }$ the Modulus. I'm partial to calling it the Quaternion Modulus (like the Complex modulus) as it avoids confusion, but this seems to be old fashioned. Any thoughts either way? --Leigh.Samphier (talk) 00:39, 27 April 2019 (EDT)


 * Definition:Quaternion Modulus is the best compromise in my eyes. Feel free to remove as many of the "field norm of Quaternion is an example of a norm which isn't" invocations on the Norm pages as you like. --prime mover (talk) 03:10, 27 April 2019 (EDT)