This is a notation question. Assume one is given two vector $\mathbf{a}$  and $\mathbf{b}$, and one constructs a third vector $\mathbf{c}$ whose elements are given by 
$$c_k=a_k b_k$$ 
Is there any standard notation for this simple operation? 
Is the notation below acceptable?
$$\mathbf{c}=\mathbf{a}\otimes \mathbf{b}$$
(Minor edits.)

It turns out that the symbol $\odot$ is often used to denote component-wise multiplication (a few examples are given in the comments below); $\circ$ and $*$ are common alternatives.
