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
  

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
  

Subscripts

The magic Function