The space Rn of the n-uples of real numbers. Vector subspace in Rn. Vector spaces, linear indipence, basis, dimension, vector subspaces. Affine subspaces in Rn. Scalar product in Rn and wedge product in R3. Matrices and their structure. Linear systems. Determinants. Linear maps, Matrix ssociated to a linear map, change of basis. Eigenvalues, eigenvectors, diagonalitation. Scalar product, symmetric operator, spectral theorem. Orthogonal and unitary operators and matrices. Canonical form of quadric and conic equations.