I often use vector math and usually make a small vector class overloading the math operators. I always lack a good option for element wise multiplication (Hadamard product). Divide becomes element wise divide, multiplication becomes the dot product and % becomes the cross product. There are no more operators with the correct precedence to overload. I suggest making another symbol, with multiplication precedence, available for overloading.
Matlab uses .* for their elementwise operations. They also use ./ and .^ so it is an established convention. But both dot and asterisk have other meanings in C++, maybe ¤ would be pretty, if we are allowed to use it.
The symbol is not that important, the important thing is to get another operator with multiplication precedence.