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