Let $x,y \in \mathbb{R}^n$
I want to represent a vector using alternative notations:
The vector is:
$$v = \begin{bmatrix} y_1/x_1 \\ y_2/x_2 \\ \vdots \\ y_n/x_n \end{bmatrix}$$
Now one way to represent this is using:
$$\begin{bmatrix} y_1/x_1 \\ y_2/x_2 \\ \vdots \\ y_n/x_n \end{bmatrix} = yx^{-1}$$
But then you will always have to preface by defining $$x^{-1}: = \begin{bmatrix} 1/x_1 \\ 1/x_2 \\ \vdots \\ 1/x_n \end{bmatrix} $$
Is there some nicer way to represent $v$? I am thinking in line of Kronecker product, Hadamard product, or some sort of outer product
$$\mbox{diag} (\mathrm x) \, \mathrm v = \mathrm y$$
Assuming that $x_i \neq 0$ for all $i \in [n]$,
$$\mathrm v = \mbox{diag}^{-1} (\mathrm x) \, \mathrm y$$