# 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