Symbol for elementwise multiplication of vectors 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?
$$\mathbf{c}=\mathbf{a}\otimes \mathbf{b}$$
 A: (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.
A: *

*Wikipedia uses $\circ$ (\circ) to denote the Hadamard product (which is the operation you describe)

*This answer makes a
good case for $\odot$ (\odot) being used instead.

A: No, I would be concerned about $\otimes$ causing confusion with the outer product (although the outer product will produce a matrix, and the componentwise product will produce a vector, so if the context is clear enough perhaps this will not be a problem).
I recommend writing componentwise multiplication of vectors using some symbol that does not have a standard meaning, perhaps $\star$ (\star) or $\diamond$ (\diamond), so that people reading won't have any preconceptions about what might be meant.
A: If I ever needed to perform a Hadamard product of two vectors $\mathbf a$ and $\mathbf b$, apart from the usual MATLAB notation (as mentioned in the first linked question in the comments), I'd probably use $\mathrm{diag}(\mathbf a)\cdot\mathbf b$, where $\mathrm{diag}(\mathbf a)$ is the diagonal matrix with diagonal entries $a_k$.
