Vectors and Arrays in M-File Environments

Summary: This module provides a totorial introduction to using vectors in an m-file environment, provieds a link to the Mathworks tutorial on MATLAB vectors and arrays, and adds a useful piece of information not covered in the tutorial.

Vectors and Arrays in M-File Environments

One significant capability of environments accounts for much of their popularity among engineers: their ability to do vector and matrix computations. M-file environments can operate on the following types of values:

• Scalar: a scalar is a single value (i.e. a number).
• Vector: a vector is an ordered series of numbers.
• Matrix: a matrix is a rectangular array of numbers.

  NOTE: 

  The ability to do computations on vectors and matrices gives MATLAB its name (MATrix LABoratory).
• String: variables may also contain strings of characters.

Vector Basics

There are several ways to create a vector of values. One is to enclose the values in square brackets. For example, the command [9 7 5 3 1] creates the vector of values 9, 7, 5, 3, and 1. This vector can be assigned to a variable v:

>> v = [9 7 5 3 1]

v =

  9  7  5  3  1

A second way to create a vector of values is with the sequence notation start:end or start:inc:end. For example, 1:10 creates the vector of integers from 1 to 10:

>> 1:10

ans =

   1   2   3   4   5   6   7   8   9  10

The command 1:0.1:2 creates the vector

>> 1:0.1:2

ans =

  1.0000  1.1000  1.2000  1.3000  1.4000  1.5000  1.6000  1.7000  1.8000  1.9000  2.0000

The command 10:-1:1 creates the vector

>> 10:-1:1

ans =

  10   9   8   7   6   5   4   3   2   1

Vector elements are accessed using numbers in parentheses. For example if the vector v is defined as v = [9 7 5 3 1], the second element of v can be accessed as

>> v(2)
    ans = 7

The fourth element of v can be changed as follows:

>> v(4) = 100

v =

    9    7    5  100    1

Element by Element Operations on Vectors

In addition to vector and matrix arithmetic, many operations can be performed on each element of the vector. The following examples use the vector v = [9 7 5 3 1].

• Addition: the command v+val adds val to each element of v:

  
  >> v+5
      ans =
  
        14  12  10   8   6
  
  

• Subtraction: the command v-val subtracts val from each element of v:

  
  >> v-5
      ans =
  
        4   2   0  -2  -4
  
  

• Multiplication: the command v*val multiplies each element of v by val:

  
  >> v*5
      ans =
  
        45  35  25  15   5
  
  

• Division: the command v/val divides each element of v by val:

  
  >> v/5
      ans =
  
        1.80000  1.40000  1.00000  0.60000  0.20000
  
  

  The command val./v divides val by each element of v:

  
  >> 5./v
      ans =
  
        0.55556  0.71429  1.00000  1.66667  5.00000
  
  

• Exponentiation: the command v.^val raises each element of v to the val power:

  
  >> v.^2
      ans =
  
        81  49  25   9   1
  
  

More Information on Vectors and Matrices

An excellent tutorial on how to use MATLAB's vector and array capabilities is at the Mathworks MATLAB tutorial page.

One useful method of accessing entire rows or entire columns of the matrix is not mentioned in the tutorial. Suppose that the matrix A is defined as

>> A = [1  2  3  4  5
        6  7  8  9  10
        11 12 13 14 15
        16 17 18 19 20]        

A = 

        1  2  3  4  5
        6  7  8  9  10
        11 12 13 14 15
        16 17 18 19 20
        

An entire row of A can be obtained by specifying a single ":" as the column index:

>> A(2,:)

    ans = 

        6  7  8  9  10

Similarly, an entire column of A can be obtained by specifying a single ":" as the row index:

>> A(:,3)

ans = 

     3
     8
    13
    18