# MATLAB - Matrix

A matrix is a two-dimensional array of numbers.

In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row.

For example, let us create a 4-by-5 matrix a

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]
```

MATLAB will execute the above statement and return the following result −

```a =
1     2     3     4     5
2     3     4     5     6
3     4     5     6     7
4     5     6     7     8
```

## Referencing the Elements of a Matrix

To reference an element in the mth row and nth column, of a matrix mx, we write −

```mx(m, n);
```

For example, to refer to the element in the 2nd row and 5th column, of the matrix a, as created in the last section, we type −

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(2,5)
```

MATLAB will execute the above statement and return the following result −

```ans =  6
```

To reference all the elements in the mth column we type A(:,m).

Let us create a column vector v, from the elements of the 4th row of the matrix a −

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
v = a(:,4)
```

MATLAB will execute the above statement and return the following result −

```v =
4
5
6
7
```

You can also select the elements in the mth through nth columns, for this we write −

```a(:,m:n)
```

Let us create a smaller matrix taking the elements from the second and third columns −

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)
```

MATLAB will execute the above statement and return the following result −

```ans =
2     3
3     4
4     5
5     6
```

In the same way, you can create a sub-matrix taking a sub-part of a matrix.

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)
```

MATLAB will execute the above statement and return the following result −

```ans =
2     3
3     4
4     5
5     6
```

In the same way, you can create a sub-matrix taking a sub-part of a matrix.

For example, let us create a sub-matrix sa taking the inner subpart of a −

```3     4     5
4     5     6
```

To do this, write −

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
sa = a(2:3,2:4)
```

MATLAB will execute the above statement and return the following result −

```sa =
3     4     5
4     5     6
```

## Deleting a Row or a Column in a Matrix

You can delete an entire row or column of a matrix by assigning an empty set of square braces [] to that row or column. Basically, [] denotes an empty array.

For example, let us delete the fourth row of a −

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a( 4 , : ) = []
```

MATLAB will execute the above statement and return the following result −

```a =
1     2     3     4     5
2     3     4     5     6
3     4     5     6     7
```

Next, let us delete the fifth column of a −

```a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(: , 5)=[]
```

MATLAB will execute the above statement and return the following result −

```a =
1     2     3     4
2     3     4     5
3     4     5     6
4     5     6     7
```

### Example

In this example, let us create a 3-by-3 matrix m, then we will copy the second and third rows of this matrix twice to create a 4-by-3 matrix.

Create a script file with the following code −

```a = [ 1 2 3 ; 4 5 6; 7 8 9];
new_mat = a([2,3,2,3],:)
```

When you run the file, it displays the following result −

```new_mat =
4     5     6
7     8     9
4     5     6
7     8     9
```

## Matrix Operations

In this section, let us discuss the following basic and commonly used matrix operations −