## Introduction to Matrix in Matlab

- Matlab stands for “Matrix Laboratory”. As we know other programming languages work on numbers at a time but Matlab works on multiple numbers at a time.
- All variables in matlab are multidimensional array.

### Matrix Formation

- First, we will see how to create an array in Matlab. An array is a row vector, so to create array commands will be X = [ 1 4 7 6 ]
- In above example, there are four elements in one row. And array name is ‘ x ’.
- An array is a one-dimensional quantity. To create matrix we need to specify a two-dimensional array, let us consider one example Matrix A is

To create the above matrix in MatLab commands will be

A = [ 4 5 6 ; 2 1 7 ; 4 0 3 ]

- In this elements are written in square brackets ( ‘ [ ] ’ ) and each row separated by semicolon ( ‘ ; ’ ) .
- Screen 1 shows the formation of a matrix that is an illustration of above example.

Screen 1: Matrix in Matlab

- Another way is to create a matrix is by using commands zeros, ones, etc.

Example : a=zeros(4,1)

A= 0

0

0

0

- Inside the brackets, 4 means 4 rows and 1 is a number of a column.

a=ones(2,3) … … … Two rows and three columns.

Ouput:

Screen 2: Matrix in Matlab

### Operations on Matrix

Below are the different operations on matrix:

#### 1. Arithmetic Operation

It allows all arithmetic operations on a matrix such as addition, multiplication, subtraction, etc

Syntax: `matrix name operator arithmetic constant`

**Example:**

If a is 4 by 4 matrix with values

4 7 3

4 2 7

8 7 2

4 2 1

In Matlab it will be represented as a = [ 4 7 3 ; 4 2 7 ; 8 7 2 ; 4 2 1 ]

a + 10

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It will give output as

14 17 13

14 12 17

18 17 12

14 12 11

For

a – 2

Output will be

2 5 1

2 0 5

6 5 0

2 0 -1

Above example shown on screen 3

Screen 3: Arithmetic operations

#### 2. Trigonometric Operations

In this, we can use all trigonometric operators like sin, cos, tan, cosec, sec, cot, sin inverse, etc

Consider one matrix B.

B =5 6 4

3 2 8

Matlab program will be

B = [ 5 6 4 ; 3 2 8 ]

sin ( B )

cos (B )

**Output is**

Screen 4: Trigonometric Operations

#### 3. Transpose of Matrix

To find the transpose of matrix a single quote ( ‘ ) is used.

Let us consider matrix X =

By applying command X ’

It will give transpose output as

Above example illustrated in screen 5

Screen 5: Transpose of Matrix

#### 4. Matrix Multiplication

We can perform matrix multiplication. By using multiplication operator we can multiply two matrix.

Let us consider X is

6 7 3 2

7 5 3 1

And transpose of X is

6 7

7 5

3 3

2 1

Matrix multiplication is given in screen 6.

Screen 6 : Multiplication of Matrix

#### 5. Power

To find power of any variable dot operator ( ‘ . ‘ ) is used before power operator ,Let us consider Matrix X = [ 6 7 3 2 ; 7 5 3 1 ]

X . ^ 3 =

216 343 27 8

343 125 27 1

#### 6. Concatenation

Concatenation is used to join two matrix together , square brackets [ ] are used for concatenation operator.

Let us consider one example Matrix A is

4 2

5 7

B= [A,A]

Output will be B

4 2 4 2

5 7 5 7

#### 7. Complex Numbers

Complex numbers are a mixture of two parts. Real part and imaginary parts, generally to represent imaginary part ‘ I ’ and ‘ j ’ variable is used.

If we put square root operation in MatLab command window ( sqrt ( -1 ) ) then it gives output as 0.0000 + 1.0000 i

Here 0 is the real part and 1 is an imaginary part.

Complex numbers representation is as follows ;

A = [ 5 + 3 i , 5 ; 2 + 2 i , 3 + 1 i ]

It is 2 by 2 matrix, the output will be

5 + 3 i 5

2 + 2 i 3 + i

Above example illustrated in screen 7

Screen 7: Complex Numbers

#### 8. Size :

This command is used to find the size of the matrix. It gives the size in the form of rows and columns. (number of rows and number of columns).

Let us consider example A = [ 5 6 8 2 ; 6 5 4 3 ; 8 7 2 2 ]

Output for size (A) will be 3 4

Here 3 represents no of rows and 4 represents no of columns.

Screen 8: Size of Matrix

### Conclusion – Matrix in Matlab

- In matrix arithmetic addition and subtraction is easy but multiplication is challenging task MatLab makes it simple and MatLab is specially designed for matrix manipulations.
- All the operations can be easily performed in MatLab such as addition, multiplication, subtraction, trigonometric functions, cross multiplication, matrix transpose, matrix inverse, complex numbers, etc

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