Similarity of Convex Bodies

This lecture covers the concept of similarity between convex bodies using the Bauech-Mazur distance to measure how similar the shapes of two compact convex bodies are. The instructor explains affine transformations, the Johen's Theover theorem, and the KKT conditions for convex functions. The lecture also delves into primal feasibility, dual feasibility, and the minimization of the log-determinant of a matrix. Additionally, the lecture explores the boundary of convex bodies and touches on the Euclidean ball. The content is illustrated with mathematical formulas and theorems.