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. Vectors in Python – A Quick Introduction!