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# Vectors in Python – A Quick Introduction!

Today, we will be having a look at one of the most unaddressed topics in Python that is, Vectors in Python. So, let us begin!

## First, what is a Vector?

A vector in a simple term can be considered as a single-dimensional array. With respect to Python, a vector is a one-dimensional array of lists. It occupies the elements in a similar manner as that of a Python list.

Let us now understand the Creation of a vector in Python.

### Creation of a Vector in Python

Python NumPy module is used to create a vector. We use numpy.array() method to create a one-dimensional array i.e. a vector.

**Syntax:**

numpy.array(list)

**Example 1: Horizontal Vector**

import numpy as np lst = [10,20,30,40,50] vctr = np.array(lst) print("Vector created from a list:") print(vctr)

**Output:**

Vector created from a list: [10 20 30 40 50]

**Example 2: Vertical Vector**

import numpy as np lst = [[2], [4], [6], [10]] vctr = np.array(lst) print("Vector created from a list:") print(vctr)

**Output:**

Vector created from a list: [[ 2] [ 4] [ 6] [10]]

### Basic Operations on a Python Vector

Having created a Vector, now let us perform some basic operations on these Vectors now!

Here is a list of the basic operations that can be performed on a Vector–

- Addition
- Subtraction
- Multiplication
- Division
- Dot Product, etc.

Let us begin!

#### 1. Performing addition operation on a Python Vector

Below, we have performed Vector addition operation on the vectors.

The addition operation would take place in an element-wise manner i.e. element by element and further the resultant vector would have the same length as of the two additive vectors.

**Syntax:**

vector + vector

**Example:**

import numpy as np lst1 = [10,20,30,40,50] lst2 = [1,2,3,4,5] vctr1 = np.array(lst1) vctr2= np.array(lst2) print("Vector created from a list 1:") print(vctr1) print("Vector created from a list 2:") print(vctr2) vctr_add = vctr1+vctr2 print("Addition of two vectors: ",vctr_add)

**Output:**

Vector created from a list 1: [10 20 30 40 50] Vector created from a list 2: [1 2 3 4 5] Addition of two vectors: [11 22 33 44 55]

#### 2. Performing Subtraction of two vectors

On similar lines, in subtraction as well, the element-wise fashion would be followed and further the elements of vector 2 will get subtracted from vector 1.

Let us have a look at it’s implementation!

import numpy as np lst1 = [10,20,30,40,50] lst2 = [1,2,3,4,5] vctr1 = np.array(lst1) vctr2= np.array(lst2) print("Vector created from a list 1:") print(vctr1) print("Vector created from a list 2:") print(vctr2) vctr_sub = vctr1-vctr2 print("Subtraction of two vectors: ",vctr_sub)

**Output:**

Vector created from a list 1: [10 20 30 40 50] Vector created from a list 2: [1 2 3 4 5] Subtraction of two vectors: [ 9 18 27 36 45]

#### 3. Performing multiplication of two vectors

In a Vector multiplication, the elements of vector 1 get multiplied by the elements of vector 2 and the product vector is of the same length as of the multiplying vectors.

Let us try to visualize the multiplication operation:

x = [10,20] and y = [1,2] are two vectors. So the product vector would be v[ ],

v[0] = x[0] * y[0]

v[1] = x[1] * y[1]

Have a look at the below code!

import numpy as np lst1 = [10,20,30,40,50] lst2 = [1,2,3,4,5] vctr1 = np.array(lst1) vctr2= np.array(lst2) print("Vector created from a list 1:") print(vctr1) print("Vector created from a list 2:") print(vctr2) vctr_mul = vctr1*vctr2 print("Multiplication of two vectors: ",vctr_mul)

**Output:**

Vector created from a list 1: [10 20 30 40 50] Vector created from a list 2: [1 2 3 4 5] Multiplication of two vectors: [ 10 40 90 160 250]

#### 4. Performing Vector division operation

In vector division, the resultant vector is the quotient values after carrying out division operation on the two vectors.

Consider the below example for a better understanding.

x = [10,20] and y = [1,2] are two vectors. So the resultant vector v would be,

v[0] = x[0] / y[0]

v[1] = x[1] / y[1]

Let us now implement the above concept.

**Example:**

import numpy as np lst1 = [10,20,30,40,50] lst2 = [10,20,30,40,50] vctr1 = np.array(lst1) vctr2= np.array(lst2) print("Vector created from a list 1:") print(vctr1) print("Vector created from a list 2:") print(vctr2) vctr_div = vctr1/vctr2 print("Division of two vectors: ",vctr_div)

**Output:**

Vector created from a list 1: [10 20 30 40 50] Vector created from a list 2: [10 20 30 40 50] Multiplication of two vectors: [ 1 1 1 1 1 ]

#### 5. Vector Dot Product

In a vector dot product, we perform the summation of the product of the two vectors in an element-wise fashion.

Let us have a look at the below.

vector c = x . y = (x1 * y1 + x2 * y2)

**Example:**

import numpy as np lst1 = [10,20,30,40,50] lst2 = [1,1,1,1,1] vctr1 = np.array(lst1) vctr2= np.array(lst2) print("Vector created from a list 1:") print(vctr1) print("Vector created from a list 2:") print(vctr2) vctr_dot = vctr1.dot(vctr2) print("Dot product of two vectors: ",vctr_dot)

**Output:**

Vector created from a list 1: [10 20 30 40 50] Vector created from a list 2: [1 1 1 1 1] Dot product of two vectors: 150

## Conclusion

By this, we have come to the end of this topic.

In order to have a deeper understanding about vectors, do try out creating a vector and performing the above mentioned operations.

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