Talk:Quaternion

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"a two-dimensional sphere"

In the section "noncommutative" the author talks about a "two-dimensional sphere". Sorry but I think you need to look at the wording here. I daren't change it to circle. —Preceding unsigned comment added by 82.69.22.206 (talk) 21:41, 21 June 2010 (UTC)[reply]

It doesn't mean a cirle; it means the two-dimensional surface of a sphere. I have changed the wording to clarify this. Gandalf61 (talk) 08:17, 22 June 2010 (UTC)[reply]

Influence upon vector calculus?

The article on vector calculus noted that vector calculus evolved out of the study of quaternions. Is this true? If so, should it be mentioned here? —Preceding unsigned comment added by 65.50.39.118 (talk) 05:50, 7 September 2010 (UTC)[reply]

See the history section, from the paragraph starting "From the mid 1880s". The wording is a little different in the other article but it's describing the same things.--JohnBlackburne^words_deeds 13:10, 22 September 2010 (UTC)[reply]

Functions of a quaternion variable

At the start of this there is a section that reads However the complications of the quaternion variable still challenge investigators. Consider for example the function - this could be expanded on, as it may not be obvious what the significance of the function mentioned is.Autarch (talk) 12:49, 22 September 2010 (UTC)[reply]

Quaternion multiplication table

Since quaternion multiplication is non-commutative, should the multiplication table at the end of 2.1 make it clear which operand is the left operand and which is the right operand? Fizzbowen (talk) 19:47, 26 September 2010 (UTC)[reply]

An excellent idea. Done! Ozob (talk) 23:14, 26 September 2010 (UTC)[reply]

"Conjugation, the norm, and reciprocal" section

The last line starts: "This makes it possible to divide two quaternions p and q in two different ways." Unless I'm missing a subtlety here, it should more accurately read "This makes it possible to depict division of two quaternions p and q in two different ways." 140.232.0.70 (talk) 17:41, 4 January 2011 (UTC)[reply]

I'm not sure what you're getting at. pq⁻¹ is not the same as q⁻¹p; for example, i⁻¹ = −i, so ji⁻¹ = −ji = ij = −i⁻¹j is not equal to i⁻¹j. That difference isn't something I'd call a "depiction". Ozob (talk) 23:45, 4 January 2011 (UTC)[reply]

two quaternions for each rotation representation

I have checked the article and discussion (and archives) but I can't seem to find anything about which quaternion to use for a given rotation. As far as I know, both "q" (angle \theta around vector p) and "-q" (angle -\theta around vector -p) represent the same rotation.

My question is as follows:

1) Is it possible to divide all quaternions into two sets without the obvious division (scalar part > 0)

2) Is there any convention of what are the "correct" quaternions?

To give some background: I am using Matlab's Aerospace Toolbox where the scalar part of a quaternion constructed from rotation angles can take any value between -1 and 1. A function I made calculates orientation from rotation angles and should produce something like a sine with the test input. There are however some jumps and I found out that my output is correct up to the sign. Now I need something to determine whether to use q or -q.

Thanks Dedekmraz (talk) 15:27, 1 March 2011 (UTC)[reply]

I would say no and no. Or at least for (1) there is none better than taking those with positive real parts. In practice usually you ignore the problem until you need to deal with it, at which point you insert a check and negate one of the quaternions to fix a discontinuity like you describe. You can check for example that the 4D dot-product between them is positive, and if not negate one. It's impossible to partition the quaternions so all are in one half as it's easy to come up with a rotation that rotates smoothly from one quaternion to −1 × itself.--JohnBlackburne^words_deeds 15:45, 1 March 2011 (UTC)[reply]

I knew I read about this dual representation somewhere. And after an hour of searching, I "decided" I read it on Wikipedia. Could be that the division was actually according to the sign of the real part. Anyway, thank you for the answer. Dedekmraz (talk) 07:15, 2 March 2011 (UTC)[reply]