Python dot product and cross product

In this Python tutorial, we will discuss the python dot product and cross product. Also, We will see these below topics as:

• What is dot product in python?
• What is Numpy and how to install NumPy in python
• Python dot product without NumPy
• Dot product in python using NumPy
• Dot product of two vectors in python
• Python compute the inner product of two given vectors
• Python dot product of 2-dimensional arrays
• Python cross product of two vectors
• Python dot product of two lists
• Python dot product of two arrays
• Python cross product of 2-dimensional arrays
• Python cross product of 3-dimensional arrays

What is Python dot product?

The Python dot product is also known as a scalar product in algebraic operation which takes two equal-length sequences and returns a single number.

What is Numpy and how to install NumPy in python

• Numpy is a python library used for working with array and matrices.
• If you have python and pip already installed on a system, then the installation of NumPy is very easy.
• Install Numpy by using the command “pip install numpy” in cmd.
• Once NumPy is installed, import it in your application by adding import numpy.

Python dot product without NumPy

If we don’t have a NumPy package then we can define 2 vectors a and b. Then use zip function which accepts two equal-length vectors and merges them into pairs. Multiply the values in each pair and add the product of each multiplication to get the dot product.

Example:

a = [5, 10, 2]
b = [2, 4, 3]
dotproduct=0
for a,b in zip(a,b):
    dotproduct = dotproduct+a*b
print('Dot product is:', dotproduct)

After writing the above code, once you will print ” dotproduct “ then the output will be ”Dot product is: 56”. It will multiply the values in each pair and add the product into final values.

You can refer to the below screenshot for python dot product without NumPy.

Dot product in python using NumPy

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.

Example:

import numpy as n
a = [5, 10, 2]
b = [2, 4, 3]
dotproduct = n.dot(a,b)
print('Dot product is:', dotproduct)

After writing the above code, once you will print ” dotproduct “ then the output will be ”Dot product is: 56”. It will calculate the dot product using the dot().

You can refer to the below screenshot for python dot product using NumPy.

Dot product of two vectors in python

Python dot product of two vectors a1 and b1 will return the scalar. For two scalars, their dot product is equivalent to a simple multiplication.

Example:

import numpy as np
a1 = 10
b1 = 5
print(np.dot(a1,b1))

After writing the above code, once you will print ” np.dot(a1,b1) “ then the output will be ” 50 ”. It will calculate the dot product using the dot().

You can refer to the below screenshot for python dot product of two vectors.

Python compute the inner product of two given vectors

An inner product is a generalization of the dot product. It is a way to multiply vectors together. By using the dot() method we can find the inner product.

Example:

import numpy as n
p
a1 = np.array([5, 6]
)
b1 = np.array([2, 5]
)
print("vectors:")
print(a1)
print(b1)
print("Inner product of vectors:")
print(np.dot(a1,b1))

After writing the above code, once you will print ” np.dot(a1,b1) “ then the output will be ”Inner product of vectors: 40”. It will compute the inner product of the vectors using the dot().

You can refer to the below screenshot for python compute the inner product of two given vectors

Python dot product of 2-dimensional arrays

If the arrays are 2-dimensional, numpy.dot() will result in matrix multiplication.

Example:

import numpy as np 
p = [[2,5],[3,2]]
q = [[1,0],[4,1]]
dotproduct = np.dot(p,q)
print(dotproduct)

After writing the above code, once you will print ” dotproduct “ then the output will be ”[[22 5] [11 2]]”. By using the dot() method it returns the matrix product of the two vectors p and q.

You can refer to the below screenshot for python dot product of 2-dimensional arrays

Python cross product of two vectors

To find the cross product of two vectors, we will use numpy cross() function.

Example:

import numpy as np
p = [4, 2]
q = [5, 6]
product = np.cross(p,q)
print(product)

After writing the above code, once you will print ” product “ then the output will be ” 14 ”. By using the cross() method it returns the cross product of the two vectors p and q.

You can refer to the below screenshot for python cross product of two vectors.

Python dot product of two lists

Python provides a very efficient method to calculate the dot product of two lists. By using numpy.dot() method, which is available in the Numpy module.

Example:

import numpy as n
list1= [10, 3, 2]
list2= [2, 5, 3]
dotproduct = n.dot(list1,list2)
print('Dot product of two list is:', dotproduct)

After writing the above code, once you will print ” dotproduct “ then the output will be ”Dot product of two list is: 41”. It will calculate the dot product of the two lists ” list1 and list2″ using the dot().

You can refer to the below screenshot for python dot product of two lists

Python dot product of two arrays

The function numpy.dot() in python returns a dot product of two arrays arr1 and arr2. The dot() product returns scalar if both arr1 and arr2 are 1-D.

Example:

import numpy as np
arr1 = np.array([2,2])
arr2 = np.array([5,10])
dotproduct = np.dot(arr1, arr2)
print("Dot product of two array is:", dotproduct)

After writing the above code, once you will print ” dotproduct “ then the output will be ”Dot product of two array is: 30”. It will calculate the dot product of the two arrays ” arr1 and arr2″ using the dot() and it will return a scalar value.

You can refer to the below screenshot for python dot product of two arrays

Python cross product of 2-dimensional arrays

To find the cross product of 2-dimensional arrays we will use numpy.cross() function of numpy library.

Example:

import numpy as np
p = [[2, 2]
, [3, 1]]
q = [[6, 7]
, [5, 4]]
product = np.cross(p,q)
print(product)

After writing the above code, once you will print ” product “ then the output will be ” [2 7] “. By using the cross() method we will get the cross product of two given vectors p and q.

You can refer to the below screenshot for python cross product of 2-dimensional arrays

Python cross product of 3-dimensional arrays

To find the cross product of 3-dimensional arrays, we will use numpy.cross() function of numpy library.

Example:

import numpy as np
p = ([3, 2, 5])
q = ([4, 7, 1]
)
product = np.cross(p,q)
print(product)

After writing the above code, once you will print ” product “ then the output will be ” [-33 17 13] “. By using the cross() method we will get the cross product of two given vectors p and q.

You can refer to the below screenshot for python cross product of 3-dimensional arrays

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In this tutorial, we learned about python dot product and Python cross product and also we have seen how to use it with an example like:

• What is dot product in python?
• What is Numpy and how to install NumPy in python
• Python dot product without NumPy
• Dot product in python using NumPy
• Dot product of two vectors in python
• Python compute the inner product of two given vectors
• Python dot product of 2-dimensional arrays
• Python cross product of two vectors
• Python dot product of two lists
• Python dot product of two arrays
• Python cross product of 2-dimensional arrays
• Python cross product of 3-dimensional arrays