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Forums
Mathematics
Calculus
Setting Up Inverse Problems
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[QUOTE="andrewkirk, post: 6008530, member: 265790"] There are two hidden assumptions embedded in the above steps: 1. The operators A and B both have inverses. 2. The inverse operators ##A^{-1}## and ##B^{-1}## commute with one another. The second one is implicitly assumed when you say: If we apply ##A^{-1}B^{-1}## to both sides of the original equation we get: $$A^{-1}B^{-1}B[f_n] = \lambda A^{-1}B^{-1} A[f_n]$$ which is $$A^{-1}[f_n] = \lambda A^{-1}B^{-1}A[f_n]$$ but we can't eliminate ##A^{-1}## and ##A## from the RHS unless ##A^{-1}## commutes with ##B^{-1}##. We run into the same difficulty if we apply ##B^{-1}A^{-1}## to both sides. Also, to number an equation set it between the delimiters \begin{[I]equation[/I]} and \end{[I]equation[/I]}. It will then be autonumbered. To number every line in a sequence of equations, use \begin{[I]align[/I]} and \end{[I]align[/I]}. I've used italics here so that the codes [I]look[/I] like codes rather than [I]functioning[/I] as codes. Don't use italics when you want to use these codes to make numbered equations. [/QUOTE]
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Forums
Mathematics
Calculus
Setting Up Inverse Problems
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