# The Colon Operator

The colon, :, is one of MATLAB’s most important operators. It occurs in several different

forms. The expression

`1:10`

is a row vector containing the integers from 1 to 10

`1 2 3 4 5 6 7 8 9 10`

To obtain nonunit spacing, specify an increment. For example,

`100:-7:50`

is

`100 93 86 79 72 65 58 51`

and

`0:pi/4:pi`

is

`0 0.7854 1.5708 2.3562 3.1416`

Subscript expressions involving colons refer to portions of a matrix.

`A(1:k,j)`

is the first k elements of the jth column of A. So

`sum(A(1:4,4))`

computes the sum of the fourth column. But there is a better way. The colon by itself

refers to all the elements in a row or column of a matrix and the keyword end refers to

the last row or column. So

`sum(A(:,end))`

computes the sum of the elements in the last column of A.

```
ans =
34
```

Why is the magic sum for a 4-by-4 square equal to 34? If the integers from 1 to 16 are

sorted into four groups with equal sums, that sum must be

`sum(1:16)/4`

which, of course, is

```
ans =
34
```