Finding Orthogonal/Orthonormal Base: First Step

This lecture covers the first step in finding an orthogonal/orthonormal base in a vector space with a scalar product, focusing on the properties of orthogonal families of vectors and the orthogonal projection of one vector onto another. The lecture also introduces the concept of projection orthogonale and its properties, providing a detailed explanation of the formulas involved. Additionally, it discusses the projection of a vector onto a subspace and its relation to the scalar product. The instructor demonstrates the application of these concepts through various propositions and proofs, emphasizing the importance of understanding orthogonal bases in linear algebra.