Linear algebra 1977/78, 1978/79. For 1st year mathematics students. Official name: Geometria I.

GROUPS, RINGS, FIELDS Sets Functions Groups and fields VECTOR SPACES The concept of basis The vector space K^n Dimension of a vector space Linear mappings MATRIX CALCULUS Coordinates in a finite-dimensional vector space The matrix associated with a linear mapping Gauss elimination Exterior algebra Systems of linear equations Eigenvectors and eigenvalues The first diagonalization theorem Matrix functions EUCLIDEAN SPACES The concept of distance Angles in R^n Distances in R^n Vector product Orthogonal mappings and rotations Orthonormal bases and Fourier coefficients Geometry of conic sections Diagonalization of symmetric matrices Normal form of conic sections Quadrics Inertial theorem