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# Vectors in Matlab

A vector is an enclosed set of elements. In Matlab, we can create vectors by using square brackets. Vectors are one of the illustrations of arrays (one-dimensional array). it can be represented in two ways row vector and column vector.

## Row Vector

It is horizontal set of elements. It is represented within square brackets. Each element is separated by comma or space.

X = [ 4 7 8 ] or X = [ 4 , 7 , 8 ]

## Column Vector

It is a vertical set of elements. It is also represented within square brackets. There are two ways to create column vectors first is by separating each element by a semicolon and another way is writing each element on the next row in the command window.

X = [ 4 ; 6 ; 7 ] or

X = [ 4

6

7 ]

## Vector Operations

Vector operators are broadly classified into two categories.

### 1. Arithmetic Operation

Let us consider two vectors x and y with values x = [ 1 4 5 3 ] and y = [ 5 3 2 1 ] we can perform various operations on these two vectors x and y.

a. Multiplication: This function is used to multiply by any arithmetic value to the entire vector.

### For Example:

mul = 3 * x

mul = 3* [ 1 4 5 3 ]

mul = [ 3 12 15 9 ]

Syntax: `variable name = arithmetic constant * vector name`

b. Trigonometric Function: We can apply any trigonometric function on vector-like sin, cos, tan, cosec, sec, etc.

Example tri = cos ( x )

Answer is : 0.54 – 0.65 0.28 -0.99

Syntax: `variable name = trigonometric function name ( vector name )`

Sum: This shows a total of (addition of ) entire elements in one vector.

### Example:

x = [ 1 4 5 3 ]

Total = sum ( x )

Output is total = 13

Syntax:`variable name = = sum ( vector name )`

c. Length: It shows length of particular vector , let us one vector p = [ 9 7 5 3 1 9 7 5 3 1 ]

### Example:

p = [ 9 7 5 3 1 9 7 5 3 1 ]

Len = length ( p )

Output is Len = 10

d. Addition of Vectors: The addition of two or multiple vectors is a simple operation in Matlab, let us consider two vectors p and q.

P = [ 4 6 3 2 ] and q = [ 5 7 9 1 ]

Output is Add = [ 9 13 12 3 ]

Syntax: `vector name operator ( + ) vector name`

Similarly, we can do subtraction operation like sub = p – q

e. Multiplication of Vectors: If we want to do multiplication of two vectors then a simple multiplication operator ( * ) will not work. Therefore we need to add a dot operator ( ‘ . ‘ ) with a multiplication operator.

### Example:

P = [ 4 6 3 2 ] and q = [ 5 7 9 1 ]

mul = p . * q

output is mul = [ 20 42 27 2 ]

Syntax: `variable name = vector name dot operator multiplication operator vector name`

Suppose I want to find out the square of one particular vector or I want to multiply the vector by that vector only.

Then syntax will be squr = x. ^ 2

## 2. Relational Operation

a. Equal to the operator: this operator compares each n every element from two vectors and gives output is zero and one form.

### Example:

m = [ 2 5 8 ]

And n = [ 5 5 3 ]

As we know there are three elements in vector m and vector n,

m == n

The above statement will give output as 0 1 0, which means first no is not equal, the second number is equal and the third no is not equal. O represents false and 1 represents true.

b. Less than operator (<): Less than the operator represents by symbol ‘ <’. we can compare a given matrix with any arithmetic constant or with any other vector.

### Example:

m = [ 3 2 4 ]

n = [ 1 1 1]

m < n

the output will be 0 0 0, which means all numbers are greater than vector n.

and if m < 10

then the output will be 1 1 1, which means all numbers are less than 10.

c. Greater than operator (>): Greater than the operator represents by the symbol ( ‘ > ’). We can compare a given matrix with any arithmetic constant or with any other vector.

### Example:

M = [ 3 2 4 ]

N = [ 1 1 1 ]

m > n

Output will be 1 1 1 ,that means all values are greater than values of vector n.