Gauss elimination method
Systems of linear algebraic equations, matrices, matrix operations, row and column operations, system matrix, extended system matrix, staircase matrix, rank of a matrix, gauss elimination method, Frobenius theorem

Determinants
Permutations, determinants, algebraic complement, properties of determinants, Cramer's rule

Inverse matrices
Unit matrix, inverse matrix, method of algebraic complements, Jordan's method

Groups
Examples of groups, group definition, commutative groups

Vector spaces
Examples of vector spaces, definition of a vector space, linear combination of vectors, generating set, basis and dimension of a vector space,

Scalar and vector products
Scalar product, vector product, mixed triple product

Orthonormal matrices
Orthonormalizing a basis, orthogonal matrices

Linear manifolds
Definition of a linear manifold, linear manifold of the solutions of a linear algebraic system

Linear transformations
Linear transfromations, linear operators

Eigenvalues, eigenvectors
Eigenvalues, eigenvectors, examples

Linear analytic geometry
General and parametric equations of straight lines and planes, special types of equations of straight lines and planes, angles between straight lines and planes, distance of apoint from a straight line and plane, bundles of straight lines, bundles of planes, bunches of plains