9. Singular Value Decomposition (SVD)

The singular value decomposition (SVD) is one of the most important matrix factorizations. It provides a numerically stable matrix decomposition that can be used for a variety of purposes and is guaranteed to exist. It can be viewed as a method of understandig the basis of the data and is used in a wide range of applications including compressing, denoising, and data reduction. Its ability to handle different types of data makes it a versatile tool in the field of data science. If you are further interested and want to know more about some applications (especially for dimensionality reduction) you can check the following Resources from Steven Brunton: http://databookuw.com/page-2/page-4/ (Youtube playlist https://www.youtube.com/watch?v=gXbThCXjZFM&list=PLMrJAkhIeNNSVjnsviglFoY2nXildDCcv and his book (Data Driven Science & Engineering Machine Learning, Dynamical Systems, and Control from Steven Brunton and J. Nathan Kutz) here: http://databookuw.com/databook.pdf where Chapter 1 is about SVD and Section 1.5 is about PCA).