Euclidean vector spaces

Scalar product, matrix expression, Euclidean norm, Cauchy Schwarz inequality, polarization and parallelogram identities
Orthogonal vectors, orthogonal and orthonormal families, Pythagorean th. of Pythagoras, expression of the scalar product in a bon, coordinates of a vector in a bon, Schmidt's orthonormalization procedure
Orthogonal subsets, ortogonal of a set, orthogonal supplementary
Orthogonal projection and projective formula, distance of a vector from a sev and application to optimization problems