The next step is to create a covariance matrix. Why are we doing this? The covariance matrix allows you to see the relationship between variables in the dataset. If some variables have a strong correlation with each other, this will allow us to avoid redundant information in the next step. This is the meaning of the PCA algorithm: to make the differences between variables more pronounced, and to get rid of information overload.

The covariance matrix is a symmetric matrix of the form nxn, where n - is the total number of measurements, i.e. variables that we have in the dataset. If we have 5 variables: `x1`, `x2`, `x3`, `x4`, `x5`, then the covariance matrix 5x5 will look like this:

Pay attention to the sign of the covariance values: if it is positive, then the variables are correlated with each other (when one increases or decreases, the second also), if it is negative, then the variables have an inverse correlation (when one increases, the second decreases and vice versa).

Let's use `numpy` to calculate the covariance matrix:

cov_mat = np.cov(X_scaled, rowvar = False) 

Let's take a look at PCA (Principal Component Analysis) from afar. In this section, you will learn what PCA is, why this data processing method is needed and see the real problems it solves.

Learn about the design of the PCA algorithm. This section will show each stage in detail and simply.

Set up your first PCA model using the Python library and solve the challenge provided for you.

Get some insights with 2D and 3D visualization of PCA results.

It's time to find out how we can explain the results. What do the first, second and third components tell us? What can we use the data for in the future?