TITLE: Notation for element-wise division of vectors
QUESTION [11 upvotes]: 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?

REPLY [8 votes]: 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 "$\odot$".