Notation for element-wise division of vectors

I am wondering if there is any standard notation for the element-wise division of vectors.

I am going to use $\oslash$ for this purpose, similar to $\odot$ that is used in some texts for element-wise multiplication. For example, assuming $\vec{u}$ and $\vec{v}$ are vectors of length $k$, then $\vec{x} = \vec{u} \oslash \vec{v}$ if $\vec{x}(i) = \vec{u}(i) / \vec{v}(i)$. Would that be strange to use this in a scientific paper?

I have no idea about standard notations regarding this operation, but I would recommend expressing $$(x_1,\ldots,x_n)\oslash(y_1,\ldots,y_n)$$ instead as $$(x_1,\ldots,x_n)\odot(\tfrac{1}{y_1},\ldots,\tfrac{1}{y_n})$$ After all, the notation $\oslash$ will not make sense unless every $y_i\neq0$.

That is known as The Hadamard division and is documented here:

https://en.wikipedia.org/wiki/Hadamard_product_(matrices)#Analogous_operations

as:

$\begin{align} C &= A {\oslash} B \\ C_{ij} &= A_{ij} / B_{ij} \end{align}$

There are some other useful Hadamard operations and notations listed there.

It is noteworthy that the Hadamard multiplication uses the symbol "$\circ$" not "$\otimes$" or "$\odot$".

Maybe you can try to take advantage of a diagonal matrix for expression: $\text{diag}^{-1}(\vec{v})\,\vec{u}$, where $\text{diag}(\cdot)$ returns a matrix with the vector as its diagonal and "$^{-1}$" means inverse of the matrix.