16. Text: What Are EigenValues & EigenVectors?
What Are Eigenvalues and Eigenvectors?
The mathematics of PCA isn't really necessary for PCA to be useful. However, it can be useful to fully understand the mathematics of a technique to understand how it might be extended to new cases. For this reason, the page has a few additional references which go more into the mathematics of PCA.
A simple introduction of what PCA is aimed to accomplish is provided here in a simple example.
A nice visual, and mathematical, illustration of PCA is provided in this video by 3 blue 1 brown.
If you dive into the literature surrounding PCA, you will without a doubt run into the language of eigenvalues and eigenvectors. These are just the math-y words for things you have already encountered in this lesson.
An eigenvalue is the same as the amount of variability captured by a principal component, and an eigenvector is the principal component itself. To see more on these ideas, take a look at the following three links below:
A great introduction into the mathematics of principal components analysis.
An example of using PCA in python by one of my favorite data scientists.