Скачать или смотреть Basic Maths of Principal Component Analysis (A beautiful gift of eigenvalues and eigenvectors)

Principal Component Analysis (PCA) identifies the directions (principal components) in the data that maximize variance, which correspond to the eigenvectors of the data’s covariance matrix. The magnitude of variance along each direction is given by the associated eigenvalue. By projecting data onto the top eigenvectors with the largest eigenvalues, PCA reduced dimensionality while retaining most of the data’s information. It is widely used for data compression, noise reduction, and visualization. The following could be usueful links:
1. Lecture notes: https://ranveeriit.github.io/files/Ba...
2. A warm-up on matrices, eigenvalues, eigenvectors and properties: https://ranveeriit.github.io/files/Wa...
3. Bad, Good, Better, Best Matrices: https://ranveeriit.github.io/files/BG... (in which category covariance matrix belongs?)
4. Why for a symmetric matrix of order nxn there always exists a set of n orthonormal eigenvectors ? https://ranveeriit.github.io/files/So... (see Theorem 2.1)