Matlab has a set of dot operators, such as .\*, ./, .^. Each of these operators consists of a dot and a normal algebraic operator. They perform element-wise algebraic operations on a matrix. For example, consider the following codes



```
A = [1 2 3; 3 2 1];
x = [1 2 4];

B = A.^2
y = 1./x

```

The result is



```
B =

     1     4     9
     9     4     1

y =

     1.0000    0.5000    0.2500

```

I find these dot operators very convenient. My question is, how to write these dot operators in mathematical expressions? (By mathematical expressions, I mean the expressions used in proofs.)


EDIT -
One obvious way is to define the result matrix element-wise. But is there a way to write this result in a more compact manner?



How to write Matlab's dot operators in mathematical expressions?
Your matrix $B$ is the Hadamard product of $A$ and $A$ which uses the notation $B = A \circ A$. However I don't know of any others, particularly for expressing $y$.


See: <http://en.wikipedia.org/wiki/Matrix_multiplication#Hadamard_product>


