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?