Mathematics

Creating Matrices

Informally, the terms matrix and array are often used interchangeably. More precisely, a matrix is a two-dimensional rectangular array of real or complex numbers that represents a linear transformation. The linear algebraic operations defined on matrices have found applications in a wide variety of technical fields. (The optional Symbolic Math Toolbox extends the capabilities of MATLAB to operations on various types of nonnumeric matrices.)

MATLAB has dozens of functions that create different kinds of matrices. Two of them can be used to create a pair of 3-by-3 example matrices for use throughout this chapter. The first example is symmetric.

• A = pascal(3)
  
  A =
         1     1     1
         1     2     3
         1     3     6
  

The second example is not symmetric.

• B = magic(3)
  
  B =
         8     1     6
         3     5     7
         4     9     2
  

Another example is a 3-by-2 rectangular matrix of random integers.

•   C = fix(10*rand(3,2))
  
    C =
         9     4
         2     8
         6     7
  

A column vector is an m-by-1 matrix, a row vector is a 1-by-n matrix and a scalar is a 1-by-1 matrix. The statements

• u = [3; 1; 4]
  
  v = [2 0 -1]
  
  s = 7
  

produce a column vector, a row vector, and a scalar.

• u =
         3
         1
         4
  
  v =
         2     0    -1
  
  s =
         7
  

Matrices in MATLAB

Adding and Subtracting Matrices

© 1994-2005 The MathWorks, Inc.