If I have two $ n \times n$ matrices, call them $[A]$ and $[B]$, where I want to divide each element by its respective element in the other matrix, what is the proper way to denote that?
I tried to solve for $[A][B]^{-1}$ but $[B]$ is not a singular matrix. Is there a proper way to denote dividing each element at a time?
To clarify, I want to signal the operation to be $A_{i,j} \div B_{i,j}$ where $i,j$ denote the row/column.
Your operation is Hadamard division. The notation $A \oslash B$ is used. But, since it's not very common, you should take quasi's advice and tell your readers what you mean by this.