I’m familiar of the inverse function notation, but I was wondering if there exists a math operator that denotes to take the inverse of something.

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    $\begingroup$ Well, the inverse of some operator $T$ is denoted $T^{-1}$, in exactly the same way that function inverses are written... I'm not sure exactly what you're looking for otherwise. $\endgroup$ – user296602 Sep 17 '18 at 21:41

If the inverse is always unique, then such an operation is often denoted by $$(\cdot)^{-1}.$$

NB: Here the dot (i.e., $\cdot$) is a sort of placeholder. It is fairly standard. What one infers from it is that one plugs an element of the domain of the operation into the place where the dot is, often omitting the brackets (that are still implied if not written); for instance, for any group $G$, we have this: $$\begin{align} (\cdot)^{-1}: G & \to G, \\ g & \mapsto g^{-1}.\end{align}$$

NB2: Sometimes inverses are not uniquely defined. See here for an example. The inverse operation is thus undefined in these instances.

  • $\begingroup$ Sometimes people don’t understand the use of the dot. Maybe you could add an example with a few different things, like scalar, matrix and function ? $\endgroup$ – Prince M Nov 23 '18 at 17:17
  • $\begingroup$ It's a notational question. There isn't much to understand. However, I'll add to this answer shortly to explain the use of $\cdot$. $\endgroup$ – Shaun Nov 23 '18 at 17:24
  • $\begingroup$ Is that better, @PrinceM? $\endgroup$ – Shaun Nov 23 '18 at 17:33
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    $\begingroup$ I think it’s a great answer $\endgroup$ – Prince M Nov 23 '18 at 23:58

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