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 moduleimport numpy as np# Taking two scalar valuesa = 5b = 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 moduleimport numpy as np# Taking two 1D arraya = 3 + 1jb = 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 moduleimport numpy as np# Taking two 2D array# For 2-D arrays it is the matrix producta = [[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 moduleimport numpy as np# Taking two 2D array# For 2-D arrays it is the matrix producta = [[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 valueprint(np.dot(b, a)) |
Output:
[[2 4] [6 9]]
