This course introduces students to the basics of linear algebra, emphasising vectors and matrices.

**Syllabus**

*Complex numbers:*

- Addition, subtraction, multiplication and division of complex numbers in both Cartesian and polar form;

- de Moivre's theorem;

- complex nth roots.

*Vectors:*

- Geometry and algebra of R^{2} and R^{3};

- vector addition and scalar multiplication.

*Matrices:*

- matrix addition and multiplication, scalar multiplication;

- systems of linear equations;

- Gaussian elimination, elementary row operations;

- identity and inverse matrices, determinants;

- eigenvalues and eigenvectors;

- diagonalization of symmetric matrices;

- applications to quadratic forms in two and three dimensions.

**On completion of the course students should be able to:**

- understand the geometric and algebraic properties of vectors in two- and three-dimensional Euclidean space;

- perform simple operations on matrices;

- solve systems of linear equations using row operations;

- calculate the determinant and the inverse of a matrix;

- calculate the eigenvalues and eigenvectors of a matrix;

- diagonalize a symmetric matrix.

- Module Supervisor: Alexei Vernitski