Geometric Transformations in R2 and R3

This lecture covers geometric transformations in R2 and R3, focusing on functions mapping vectors to their transformations, including reflections and rotations. The instructor demonstrates how to determine the expression of a transformation function and the inclination of axes. The lecture also explores the concept of symmetry and orthogonal reflections, providing step-by-step examples of applying transformations in practical scenarios, such as billiards. Through detailed explanations and mathematical derivations, students will gain a solid understanding of how geometric transformations operate in different dimensions.