# Introduction to Vectors and Matrices in Matlab

## 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```