Talk:Commutator

message: What does this statement mean?
In linear algebra, if two matrices commute in one basis they will commute in any basis.
It seems to be trying to mean that, if A and B are the matrices of two linear operators with respect to one basis, and A' and B' are the matrices of the same two operators (in the same order) with respect to another basis, then A and B commute if and only if A' and B' do.  However, the statement as it stands is meaningless.  JadeNB 21:18, 10 October 2006 (UTC)
thread_title:  Matrices in bases 

message: The standard mathematical notation for commutator is \scriptstyle{ad(x)(y)=[x,y]}. As I see no reason to depart from the standard, I changed the relevant paragraph.
AlainD 10:02, 25 January 2007 (UTC)
thread_title:  Standard notation 

message: I think it's misleading to use the notation "ad(x)^3(y) = [x,[x,[x,y]]]", since there are a lot of different algebras floating around. In particular, ad(x) is a derivation, which has both the usual algebra structure of composition, and a Lie algebra structure induced from the former. Of course y lives in a Lie algebra, where something like y^3 is not defined. I admit that ad(x) may be unambiguous mathematically, but I feel that in this context it's best to avoid confusion if possible. Tesseran 07:46, 28 June 2007 (UTC)
thread_title:  notation for ad(''x'')ad(''x'')(''y'') 

message: I suggest that we add a brief section or one-liner about the anticommutator: {A,B} := AB + BA since this notation is not mentioned in the anticommutativity article and comes up a lot (at least in physics).  Cheers A13ean (talk) 22:50, 5 October 2008 (UTC)
replies: text: Agreed (especially since anticommutator redirects here). I made a quick start, feel free to flesh it out a bit. --Strange but untrue (talk) 17:34, 10 November 2008 (UTC)
thread_title:  Brief section about the anticommutator 

message: In the Ring theory section, mention is made of the connection between the commutator, the Heisenberg uncertainty principle and the Robertson-Schrödinger relation.  This discussion is clearly from Liboff, I have a copy and I have located the subject matter in the text, but my copy is the 2nd edition, not the 4th edition listed in the References section of the article.  Would someone who has access to the 4th edition please update the page number of the reference? — Anita5192 (talk) 05:13, 25 March 2012 (UTC)
replies: text: Nevermind.  I just looked up a copy in the library and fixed this myself. — Anita5192 (talk) 04:51, 27 July 2012 (UTC)
thread_title:  Reference needed for uncertainty principle 

message: Should Ring commutator redirect here?  — Preceding unsigned comment added by 70.247.173.205 (talk) 04:56, 1 March 2016 (UTC)
thread_title:  Ring commutator 

message: The section on ring identities is strange and confusing, in that it launches straight into Lie algebra identities, without developing any other results first.  Where are the finite rings?  Why jump straight to algebras?  Maybe this section needs a new heading?  Perhaps more identities can be found for these cases?  — Preceding unsigned comment added by 70.247.173.205 (talk) 05:00, 1 March 2016 (UTC)
thread_title:  Ring identities 

message: The third property is redundant because [A + B, C] and [A, A] = 0 imply it. This is according to Abraham and Marsden's Foundations of Mechanics. Should we get rid of property 2 or 3, or put it in under the commutator identities?
MichalKononenko (talk) 05:18, 18 January 2018 (UTC)
thread_title:  Ring Theory Lie Algebra Identities 

message: Property no. 4 in the Lie Algebra identities (https://en.wikipedia.org/wiki/Commutator#Lie-algebra_identities) is either plain wrong and inconsistent with, say, the initial identity under Additional Identities (i.e. [AB,C] = A[B,C]+B[A,C]) or it requires a much better explanation of why and when it holds.
Episanty (talk) 21:07, 18 August 2018 (UTC)
replies: text: I don't know what you are referring to.  The identity [AB,C] = A[B,C] + B[A,C] is nowhere in the article, but [A,BC] = [A,B]C + B[A,C] and [AB,C] = A[B,C] + [A,C]B are in the article, and both are correct.—Anita5192 (talk) 00:22, 19 August 2018 (UTC)
replies: text:  The identity [AX+BY,Z]=A[X,Z]+B[Y,Z], currently numbered no. 5 at https://en.wikipedia.org/wiki/Commutator#Lie-algebra_identities, is either (a) completely wrong, or at very best (b) out of place and with missing assumptions. As to why it's considered acceptable to remove a flag for attention without getting due clarification first, I'm completely in the dark. Episanty (talk) 18:03, 20 August 2018 (UTC)
replies: text: You were right about number 5.  Thank you for pointing this out.  Number 6 was also incorrect.  I have removed them.—Anita5192 (talk) 21:23, 20 August 2018 (UTC)
thread_title:  Lie-Algebra identities