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

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