Is there a notation for element-wise (or pointwise) operations?
For example, take the element-wise product of two vectors x and y (in Matlab, x .* y, in numpy x*y), producing a new vector of same length z, where $z_i = x_i * y_i$ .
In mathematical notation, there doesn't seem to be a standard for this, am I wrong?
There is $x \cdot y$, the dot product. There is $x*y$, which is usually considered the cross product. I need to find a notation for element-wise multiplication. I was aiming at maybe using the . as is done in Matlab, but it looks a little off :
$z = x .* y$
What do you think?
Best Answer
I've seen several conventions, including $\cdot$, $\circ$, $*$, $\otimes$, and $\odot$. However, most of these have overloaded meanings (see http://en.wikipedia.org/wiki/List_of_mathematical_symbols).
Thus, in my personal experience, the best choice I've found is:
Also:
Thus I recommend $\odot$, as it is the only option I have yet to come across that has seems to have no immediate drawbacks.