Talk:Octonion

message: I removed a remark: "Hamilton invented the word associative so that he could say that octonions were not associative."
In  this was credited to Cayley, then  and moved before the citation, which does not involve the term "associative" at all. This makes me suspect it wasn't meant very seriously.
Graves wrote to Hamilton about his "octaves" on December 26, 1843 (according to Hamilton's account:
* 
but Hamilton was already using the term "associative character" to talk about quaternions in his paper presented November 13, 1843:
* .
Hopefully this is sufficient explanation to remove the remark rather than sticking a citation request on it. Agashlin (talk) 12:16, 2 May 2017 (UTC)
replies: text: Just wanted to add that I regret having written an uncharitable summary for that edit, I don't think there was malicious intent and I should have assumed good faith anyway. Agashlin (talk) 12:44, 2 May 2017 (UTC)
replies: text: Since this ia a Talk page, references stay in sections. — Rgdboer (talk) 21:16, 11 October 2017 (UTC)
thread_title:  Invention of "associative" 

message: first it was stated:
Just as quaternions can be defined as pairs of complex numbers, the octonions can be defined as pairs of quaternions
and next time you wrote:
Because of their non-associativity, octonions do not have matrix representations, unlike quaternions.
but if a quaternion can be represented by a matrix, and octonions can be defined as 4 quaternions
then it could be represented uniquely by 4x4x4 (3D) matrix.. No? — Preceding unsigned comment added by Xakepp35 (talk • contribs) 
: You should look at the Cayley–Dickson construction. It is how each of the algebras is derived from the previous one, so how octonions is derived from quaternions. And because of how it works each time the new algebra loses certain properties. As you move from quaternions to octonions you lose associativity, so there is no matrix representation (as matrices are associative).--JohnBlackburnewordsdeeds 06:28, 11 October 2017 (UTC)
replies: text: I guess the question is "what do you mean by matrix representation?" Obviously it is not a subalgebra of a matrix ring because any such algebra is associative.  But the elements of any finite dimensional algebra can be viewed as a linear transformation and therefore a square matrix.  This is, at least, the spirit of Jacobson's structural description of general finite dimensional algebras.  That being the case, I'm rewording to be more explicit about the assumption that was previously made: that a 'matrix representation' meant "subalglebra of a matrix ring". Rschwieb (talk) 15:01, 8 January 2021 (UTC)
thread_title: Matrix representation

message: English next time please??? Carlimited (talk) 03:29, 16 December 2022 (UTC)
replies: text: Could you be specific, please? It would be easier to address your issue if you made it clear.—Anita5192 (talk) 06:34, 16 December 2022 (UTC)
thread_title:  Huh??? 

message: One of the graphs stick out past the Tools bar. I don't know how to fix this, could someone else do it? UnqaidIntern (talk) 17:13, 16 May 2023 (UTC)
replies: text: They look fine to me. Which graph are you referring to?—Anita5192 (talk) 17:21, 16 May 2023 (UTC)
replies: text: It's the IJKL graph, I'm on a Chromebook so that might be the reason. UnqaidIntern (talk) 17:23, 16 May 2023 (UTC)
replies: text: I see what you mean. The diagram should be replaced by separate, smaller diagrams, but I don't have the facilities for doing that. Hopefully someone else will.—Anita5192 (talk) 18:10, 16 May 2023 (UTC)
replies: text: Much easier to simply reduce the image size - fixed.Jgmoxness (talk) 15:44, 7 August 2023 (UTC)
thread_title:  UI problem 

message: At the top of the page, it says of the octonions "they are alternative. They are also power associative." This is technically correct, but the language suggests that alternativity and power associativity are independent. They aren't - power associativity is a weaker form of (and thus prerequisite to) alternativity. This should probably be rephrased to something like "they are alternative, and thus power associative", but I can't find the best way to phrase that sentence. Cyversch (talk) 19:04, 13 May 2024 (UTC)
thread_title:  Alternativity implies power associativity