Introduction to Vectors and Matrices in Matlab

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Introduction to Vectors and Matrices in Matlab

As you know Matlab is the short form of Matrix Laboratory. As its name indicates, Matlab makes matrix and vector operations very easy. I am writing this tutorial on the assumption that you are familiar with Matlab, if not please goto the first tutorial.

Creating Row Matrix or Row Vector

Let’s start with a simple example for creating a row vector or row matrix with elements 1, 2, 3, 4, 5 and is assigned to a variable name A.

>> A = [1 2 3 4 5]
A =
1 2 3 4 5

In the above example we used equal sign (=) for assigning variable name, square brackets ([]) to enclose elements and space to separate ( ) elements. You can also use coma (,) for separating elements instead of space ( ).

Creating Column Matrix or Column Vector

Semicolon (;) is used to distinguish between rows and can define a colum vector in the following way.


>> A = [1;2;3]
A =
1
2
3

or you can write

>> A = [1
2
3]
A =
1
2
3

Transpose

Transpose of a matrix or a vector can be find using single quote (‘) as shown below.

>> A = [1 2 3]
A =
1 2 3

>> A'
ans =
1 
2 
3

 Defining a 3×3 Matrix

You can define a 3×3 matrix in any of the following ways.

>> A = [1 2 3; 4 5 6; 7 8 9]
>> A = [1 2 3
4 5 6
7 8 9]
>> A = [[1 4 7]' [2 5 8]' [3 6 9]']

All of the above command have same result as shown below.



A =
1 2 3
4 5 6
7 8 9

Defining Vectors with Repetitive Pattern

Matlab has a facility to create large vectors easily, which having elements with repetitive pattern by using colons (:). For example to create a vector whose first element is 1, second element is 2, third element is 3, up to 8 can be created by the following command.

>>  v = [1:8]
v =
1 2 3 4 5 6 7 8

If you wish to have repetitions with increment other than 1, then you have to specify starting number, increment and the last number as given below.

>> v = [1:2:8]
v =
1 3 5 7

Accessing Elements within a Vector or Matrix

Any element of a vector or matrix can be accessed through indexing as in every programming languages as shown below. Unlike C, C++ and Java, array index starts from 1.

>> a = [1 2 3 4];
>> a(3)
ans =
3
>> b = [1 2 3; 4 5 6; 7 8 9];
>> b(2,3)
ans =
6

Semicolon (;) is used to suppress output as described in the first tutorial.



Extracting Submatrices from a Matrix

Matlab also have the facility to extract submatrices from a matrix as shown in the below example.

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

This example creates a submatrix of matrix a containing elements of rows 2 to 4 and columns 1 to 3.

You can extract entire row or column in the following way.

>> A(:,2)
ans =
2
7
12
17
>> A(2,:)
ans =
6 7 8 9 10

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