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
