Getting Started

Arrays

When they are taken away from the world of linear algebra, matrices become two-dimensional numeric arrays. Arithmetic operations on arrays are done element-by-element. This means that addition and subtraction are the same for arrays and matrices, but that multiplicative operations are different. MATLAB uses a dot, or decimal point, as part of the notation for multiplicative array operations.

The list of operators includes

+	Addition
-	Subtraction
.*	Element-by-element multiplication
./	Element-by-element division
.\	Element-by-element left division
.^	Element-by-element power
.'	Unconjugated array transpose

If the Dürer magic square is multiplied by itself with array multiplication

• A.*A
  

the result is an array containing the squares of the integers from 1 to 16, in an unusual order.

• ans =
     256     9     4   169
      25   100   121    64
      81    36    49   144
      16   225   196     1
  

Building Tables

Array operations are useful for building tables. Suppose n is the column vector

• n = (0:9)';
  

Then

• pows = [n  n.^2  2.^n]
  

builds a table of squares and powers of 2.

• pows =
       0     0     1
       1     1     2
       2     4     4
       3     9     8
       4    16    16
       5    25    32
       6    36    64
       7    49   128
       8    64   256
       9    81   512
  

The elementary math functions operate on arrays element by element. So

• format short g
  x = (1:0.1:2)';
  logs = [x log10(x)]
  

builds a table of logarithms.

•  logs =
        1.0            0 
        1.1      0.04139
        1.2      0.07918
        1.3      0.11394
        1.4      0.14613
        1.5      0.17609
        1.6      0.20412
        1.7      0.23045
        1.8      0.25527
        1.9      0.27875
        2.0      0.30103
  

More About Matrices and Arrays

Multivariate Data