Learn about Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) in this comprehensive lecture from the University of Utah's Data Science program. Begin with a thorough exploration of multicollinearity before diving into the core concepts of PCA and its applications in dimensionality reduction. Master key mathematical concepts including vector basis and projection techniques. Understand how SVD works, its optimization of Sum of Squared Errors (SSE), and practical applications through rank k-approximation. Conclude with a hands-on demonstration that reinforces theoretical concepts with practical implementation. Perfect for data science students and practitioners looking to enhance their understanding of fundamental dimensionality reduction techniques.