Orthogonal Projections and Reflections in 2D

This lecture covers the geometric description of orthogonal projections and reflections in 2D, focusing on transformations such as orthogonal projection onto a line and reflection across an axis. It explains how these transformations preserve lengths, areas, and geometric angles, while also discussing their bijectivity and properties related to fixed points. The lecture further delves into the analytical expressions for these transformations, illustrating them with examples and providing insights into matrices of reflections and projections. Additionally, it explores the characterization of symmetric matrices and their properties, including trace and determinant. The lecture concludes with a discussion on diagonalizable matrices and their eigenvectors.