# Notation for element-wise multiplication of vector and matrix columns

What is a clear and concise notation for the element wise multiplication (Hadamard product) of a column vector $$v$$ and each column of a matrix $$F$$.

What I want to achieve it this: $$v\odot F= \begin{bmatrix} v_1\\ v_2 \\ v_3 \end{bmatrix} \odot \begin{bmatrix} f_{1,1} & f_{1,2} & f_{1,3}\\ f_{2,1} & f_{2,2} & f_{2,3}\\ f_{3,1} & f_{3,2} & f_{3,3} \end{bmatrix} = \begin{bmatrix} v_1f_{1,1} & v_1f_{1,2} & v_1f_{1,3}\\ v_2f_{2,1} & v_2f_{2,2} & v_2f_{2,3}\\ v_3f_{3,1} & v_3f_{3,2} & v_3f_{3,3} \end{bmatrix}$$

My question is essentially the same as this one, but I don't think the answer there actually answers the question and I don't have enough reputation to comment.

I would tend to write this as $$P = diag(v) F$$ having first defined $$diag: \Bbb R^n \to M_{nn}$$ as clearly as possible.