The Colon Operator :: Matrices and Arrays (Getting Started)

Getting Started

The Colon Operator

The colon, :, is one of the most important MATLAB 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
```

100    93    86    79    72    65    58    51

and

```
0:pi/4:pi
```

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
```

Subscripts The magic Function