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I have seen questions on Math.SE what is the typical notation for coordinatewise vector multiplication (Hadamard product), but I haven't found an answer to case of exponentiation.

Given a vector $v=(v_1,v_2,v_3)$, how would one write the vector $(e^{v_1},e^{v_2},e^{v_3})$? The same goes for matrices.

My current solution is an abuse of notation: $e^v$. Similarly, I use $\log{v}$ or $\frac{1}{v}$ and so on.

One example where you could run into such a scenario: Sometimes we would like to exchange a linear system $Ax=b$ with a log-linear system, which one could write (in my current notation) as $e^{Ax}=b$.

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