*53*

The **Euclidean distance** between two vectors, A and B, is calculated as:

**Euclidean distance = âˆšÎ£(A _{i}-B_{i})^{2}**

To calculate the Euclidean distance between two vectors in Python, we can use theÂ **numpy.linalg.norm** function:

#import functions import numpy as np from numpy.linalg import norm #define two vectors a = np.array([2, 6, 7, 7, 5, 13, 14, 17, 11, 8]) b = np.array([3, 5, 5, 3, 7, 12, 13, 19, 22, 7]) #calculate Euclidean distance between the two vectors norm(a-b) 12.409673645990857

The Euclidean distance between the two vectors turns out to beÂ **12.40967**.

Note that this function will produce a warning message if the two vectors are not of equal length:

#import functions import numpy as np from numpy.linalg import norm #define two vectors a = np.array([2, 6, 7, 7, 5, 13, 14]) b = np.array([3, 5, 5, 3, 7, 12, 13, 19, 22, 7]) #calculate Euclidean distance between the two vectors norm(a-b) ValueError: operands could not be broadcast together with shapes (7,) (10,)

Note that we can also use this function to calculate the Euclidean distance between two columns of a pandas DataFrame:

#import functions import pandas as pd import numpy as np from numpy.linalg import norm #define DataFrame with three columns df = pd.DataFrame({'points': [25, 12, 15, 14, 19, 23, 25, 29], 'assists': [5, 7, 7, 9, 12, 9, 9, 4], 'rebounds': [11, 8, 10, 6, 6, 5, 9, 12]}) #calculate Euclidean distance between 'points' and 'assists' norm(df['points'] - df['assists']) 40.496913462633174

The Euclidean distance between the two columns turns out to be **40.49691**.

**Notes**

**1.Â **There are multiple ways to calculate Euclidean distance in Python, but as this Stack Overflow thread explains, the method explained here turns out to be the fastest.

**2.Â **You can find the complete documentation for the **numpy.linalg.norm** function here.

**3.** You can refer to this Wikipedia page to learn more details about Euclidean distance.