What is covariance matrix?

The covariance matrix gives us information about the covariances between random variables. If there are two random variables X and Y, then the covariance matrix of X and Y is denoted as:

Similarly, if there are three random variables X, Y, and Z, then the covariance matrix of X, Y, and Z will be:

How to calculate covariance matrix using Python?

We can use the numpy module in Python to calculate covariance matrix between random variables.

from numpy import cov
 
data1 = [1, 2, 3, 4, 5]
data2 = [6, 7, 8, 9, 10]
 
print(cov(data1, data2, ddof=1))

Please note that here we are calculating the sample covariance, and hence, the delta degrees of freedom or ddof is 1. As a result, (n-1) is used as the denominator. If the delta degrees of freedom or ddof is 0, then n will be used in the denominator instead of (n – 1) to calculate the covariance.

The output of the above program will be:

[[2.5 2.5]
[2.5 2.5]]