Convex Optimization: Notation and Matrix Norms

This lecture covers the notation used in Convex Optimization, including the representation of scalars, vectors, and matrices. It also delves into the concept of convex sets and functions, emphasizing the definition and properties of convex functions. Additionally, the lecture explores vector norms, focusing on the p-norm and its properties. The presentation continues with discussions on unit basis vectors, dot products, and eigenvalues. The lecture concludes with topics such as the trace of a matrix, principal minors, and the rank of a matrix, providing insights into the fundamental concepts of linear algebra in the context of optimization.