- Vector spaces over the field and their subspaces. Intersections and linear, resp. direct sums. Linear combination of vectors, spanning sets, linear dependence and independence. Steinitz theorem, basis and dimension of a vector space.

- Matrix over a field, type and rank of a matrix. Operations with matrices, transposed, inverse, regular and singular matrices.

- Systems of linear equations over a field, homogeneous and nonhomogeneous, solvability.

- Permutations. Determinant of a matrix. Cofactors and adjoints. Laplace expansion. Determinants and matrix inverses. Cramer rule.

- Linear mapping, composed and inverse mapping.

- Scalar and vector products.

The basic course focusing on vector spaces, matrices, systems of linear equations, determinants and linear mappings. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.