1. describe and apply linear algebra basic concepts and methods
2. demonstrate fundamental skills of matrix calculus and solving linear systems of equations
3. apply fundamental knowledge of vector analysis and space analytic geometry
4. demonstrate basic knowledge of vector spaces and linear operators
5. demonstrate an ability to express mathematical ideas and abstract thinking in linear algebra
6. demonstrate an ability to basic problem solving and reaching conclusions in linear algebra
7. use methods of linear algebra in engineering

Lectures are held in two cycles, 4 hours per week

Exercises are held in two cycles, 4 hours per week

Homework is accessible on course web-page.

1. Matrices; Basic types; Operations with matrices; Inverse matrix; Regular and singular matrices
2. Determinants; Basic properties, computation of determinants; Laplace's rule, Elementary transformations, rank of a matrix, linear independence and rank; Characterization of regular matrices
3. Elementary transformations, rank of a matrix, linear independence and rank; Characterization of regular matrices, Characterization of regular matrices using determinant; Computation of the inverse matrix
4. Gaussian elimination method; Homogeneous and nonhomogeneous systems, Rank of a system and rank of extended matrix
5. Rank of a system and rank of extended matrix, Cramer's rule; Comparison of computational complexity of the Gauss and Cramer algorithms
6. Operations with vectors; Linear dependence and independence in V^2 and V^3; Bases in V^2 and V^3; Canonical base; Vectors in coordinate systems, Dot product; Norm, ortogonality; Vector and scalar projections of one vector on another
7. Cross product of two vectors and mixed product of three vectors, Radius-vector; Coordinates of the midpoint of a segment and of the barycenter of a triangle; Convex combinations of vectors; Convex hull; Convex set
8. Midterm exam
9. Equations of plane; Mutual position of two planes; Distance between a point and a plane
10. Line, parametric and canonical equations; Mutual position of a line and a plane
11. Vector spaces and their subspaces; Linear hull (span); The space R^n, Linear independence and dependence; Basis and dimension
12. Coordinate system; Basis change; Transition matrix, Inner product; Inner product space; Orthogonal basis; Fourier coefficient; Orthogonal projection; Normed vector space
13. Linear operators and their matrix representation; Basis change; Similar matrices, Examples of linear operators in V^2 and V^3; Linear functional; Hyperspace, half-space
14. Eigenvalues and eigenvectors; Eigenspaces; Characteristic polynomial; Hamilton-Cayley's theorem, Schur's theorem; Matrix functions; Spectral mapping theorem
15. Final exam