Principal component analysis (PCA) is a mathematical tool. It is used to analyze data components by weight. data distribution. It is widely used to change the basis of data and / or measurements. ionic reduction. Determine the main components and their weights. Eigenvalues and eigenvectors are used.

(a) Investigate and explain in detail what the roles of eigenvalues and eigenvectors are in the PCA.

(b) Write the Python code for the PCA. For this purpose, you are not allowed to use the built-in functions for PCA. Please add comments to your code.