Isometries in Euclidean Spaces

This lecture covers the concept of isometries in Euclidean spaces, which are bijective transformations that preserve distances. Examples include translations and rotations around a fixed point. The lecture also discusses orthogonal symmetry as a linear isometry. Various properties and proofs related to linear isometries are presented, along with the notion of affine transformations. The lecture concludes with a detailed exploration of matrices and their role in defining isometries.