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