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


Complex numbers:
- Addition, subtraction, multiplication and division of complex numbers in both Cartesian and polar form;
- de Moivre's theorem;
- complex nth roots.

- Geometry and algebra of R2 and R3;
- vector addition and scalar multiplication.

- 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.