Course content

The course includes: general vector spaces (linear independence, basis), spaces with inner product, orthonormal basis, Gram-Schmidt, change of basis, orthogonal matrices, linear
transformations (kernel, image, dimension theorem, associated matrices), eigenvalues and eigenvectors for linear transformations and matrices, eigenspaces, complex vector spaces, complex inner products, unitary and Hermitian matrices, singular value decomposition and Cayley-Hamilton's theorem. Several applications, among others; Markov chains, population growth (Leslie matrices), genetics.

Learning outcome

The aim of the course is to give an introduction to abstract vector spaces, and to show how thise can be applied to solve practical problems.

Learning methods and activities

Lectures and exercises. The assessment of the student is given through a written final examination by the letter grading system.

Compulsory assignments

• Exercises

Recommended previous knowledge

MA1201 Linear algebra and geometry.

Course materials

Will be announced at the start of the course.

Credit reductions