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