# 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 m^{th} row and n^{th} column, of a matrix *mx*, we write:

mx(m, n);

For example, to refer to the element in the 2^{nd} row and 5^{th} 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 m^{th} column we type A(:,m).

Let us create a column vector v, from the elements of the 4^{th} 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 m^{th} through n^{th} 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: