Eigenvalues and Eigenvectors
Probably the most important lecture in this course -- we start from the calculation of eigenvalues and eigenvectors, and move on to related topics such as the eigendecomposition, singular value decomposition, and the Moore-Penrose inverse.
This long post covers the quadratic form and the positive definiteness of matrices. The decomposition of symmetric matrices is slightly touched on, and the entire post is mainly to prepare for the next chapter -- eigenvalues and eigenvectors.
Decomposition and Smoothing Methods
Decomposition procedures to extract trend, seasonal and other components from a time series. Smoothing techniques like moving average and Lowess are often used, and exponential smoothing (Holt-Winters) is another powerful tool.