How to calculate dot product of two vectors in Python?

In mathematics, the dot product or also known as the scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. Let us given two vectors A and B, and we have to find the dot product of two vectors.

Given that, 

and,

Where,

i: the unit vector along the x directions

j: the unit vector along the y directions

k: the unit vector along the z directions

Then the dot product is calculated as:

Example:

Given two vectors A and B as,

Dot Product of Two Vectors in Python

Python provides a very efficient method to calculate the dot product of two vectors. By using numpy.dot() method which is available in the NumPy module one can do so.

Syntax:

numpy.dot(vector_a, vector_b, out = None)

Parameters:

vector_a: [array_like] if a is complex its complex conjugate is used for the calculation of the dot product.

vector_b: [array_like] if b is complex its complex conjugate is used for the calculation of the dot product.

out: [array, optional] output argument must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b).

Return:

Dot Product of vectors a and b. if vector_a and vector_b are 1D, then scalar is returned

Example 1:

Python

# Python Program illustrating
# dot product of two vectors

# Importing numpy module
import numpy as np

# Taking two scalar values
a = 5
b = 7

# Calculating dot product using dot()
print(np.dot(a, b))

Output:

35

Example 2:

Python

# Python Program illustrating
# dot product of two vectors

# Importing numpy module
import numpy as np

# Taking two 1D array
a = 3 + 1j
b = 7 + 6j

# Calculating dot product using dot()
print(np.dot(a, b))

Output:

(15+25j)

Example 3:

Python

# Python Program illustrating
# dot product of two vectors

# Importing numpy module
import numpy as np

# Taking two 2D array
# For 2-D arrays it is the matrix product
a = [[2, 1], [0, 3]]
b = [[1, 1], [3, 2]]

# Calculating dot product using dot()
print(np.dot(a, b))

Output:

[[5 4]
 [9 6]]

Example 4:

Python

# Python Program illustrating
# dot product of two vectors

# Importing numpy module
import numpy as np

# Taking two 2D array
# For 2-D arrays it is the matrix product
a = [[2, 1], [0, 3]]
b = [[1, 1], [3, 2]]

# Calculating dot product using dot()
# Note that here I have taken dot(b, a)
# Instead of dot(a, b) and we are going to
# get a different output for the same vector value
print(np.dot(b, a))

Output:

[[2 4]
 [6 9]]