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This question may be too broad. But I really want to know some concrete explanations. I often find various commutations appear here and there, which concerns the application order of two operators. For examples, between exterior calculus of the differential forms and discretization, optimization-then-discretization or discretization-then-optimization, and inner-outer iterations. Do you have some understanding of concrete examples where the commutation plays an important role?

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It's important what part of the expression is continuous. This as a hint. – vanCompute Feb 16 '13 at 22:14
Could you refine your question? I cannot connect the dots from commutative operators to what you say about differential forms. – seb Feb 17 '13 at 7:52

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