Notation for Element-Wise Matrix Operations

[OhMyMarkov]

Hello everyone!

Is there a conventional notation for some common arithmetic operations, like element-wise product, or element-wise power?

Thanks!

 

[Ackbach]

Re: Notation for Eelement-Wise Matrix Operation

I would probably just refer to indices. So if you have a matrix $A$, the $i,j$ element is $A_{ij}$. If you have another matrix $B$ of the same dimensions, then you could do element-wise exponentiation like this:

$$A_{ij}^{B_{ij}}.$$

Also note that in the MATLAB software and various clones, you can use a period prefix to indicate element-wise arithmetic, like .* for element-wise multiplication.