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 two.

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

Linear Algebra

Multivariate Data