Lecture
This lecture covers the concepts of orthogonal families and orthonormal families in a vector space with a scalar product. An orthogonal family has inner products equal to zero, while an orthonormal family has inner products equal to one. The lecture also discusses bases, coordinates, and properties of orthogonal and orthonormal bases. Examples are provided to illustrate these concepts, including the standard scalar product in Euclidean spaces. The lecture concludes with proofs and verifications related to orthogonal and orthonormal bases.