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45m
revised Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
Added reverse steps from matrices back to symbols
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awarded  Nice Answer
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revised Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
Different definition with the same properties used. Gives different result.
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revised Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
Motivation
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revised Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
copied wrong defininitions
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revised Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
Error copying equation
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answered Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
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comment Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
I would do this without NonCommutativeMultiply altogether. But if you do want to go that route, I think you will have to provide the code that you tried for your commutator algebra. Otherwise we'd have to re-invent the wheel before answering.
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reviewed Close Parametric Plot 3D won't show up
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revised Why doesn't FullSimplify simplify expressions with DiracDelta?
small clarification
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revised Why doesn't FullSimplify simplify expressions with DiracDelta?
Added more explanation
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comment Why doesn't FullSimplify simplify expressions with DiracDelta?
@NikkiBisschop I edited my answer to include more examples, and what I say in the first paragraph of the edit is based on your comment. It is in fact the answer to your overarching question why DiracDelta isn't simplified as such. One needs the information identifying the integration variable to make the correct simplification.
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comment Why doesn't FullSimplify simplify expressions with DiracDelta?
@Dr.WolfgangHintze I just checked in version 8.0.4, and I cannot reproduce your problem. It simplifies correctly on my system, even in the older version. This is on Mac OS 10.7.5.
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comment Why doesn't FullSimplify simplify expressions with DiracDelta?
@Dr.WolfgangHintze Ah, so this time it was good that I used version 10.0.1. There, it does simplify exactly to what you quoted...thanks for pointing out the issue with 8!
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comment Why doesn't FullSimplify simplify expressions with DiracDelta?
@Dr.WolfgangHintze I did find a shortcoming when I switched the variables in your example and replaced the square by a symbolic n - see my edit. But I think one gets pretty decent results all in all.
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revised Why doesn't FullSimplify simplify expressions with DiracDelta?
Added more examples and a caveat
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revised Why doesn't FullSimplify simplify expressions with DiracDelta?
Added more examples
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comment Why doesn't FullSimplify simplify expressions with DiracDelta?
@Dr.WolfgangHintze Well, you get the correct answer. There is no problem at all. @Nikki Yes, the notation of the Dirac delta function is sometimes ambiguous because it doesn't include the info as to which variable is the integration variable. This can only be fixed by stating that information in the (Inverse)FourierTransform.
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answered Mathematica 8 remove black background from image
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comment Why doesn't FullSimplify simplify expressions with DiracDelta?
@BobHanlon Yes, that's right, either way is fine (and if for some reason one way doesn't work, you can always try the other order to make sure).