Course content

Metric spaces, completeness and the contraction principle. Picard's theorem and Jacobi iteration. Recapitulation of linear algebra. Inner product spaces, projections and least squares problems. The spectral theorem and Jordan decomposition. The Cayley-Hamilton theorem. Positive definite matices, pseudo inverse and singular value decomposition. Banach spaces and Hilbert spaces. Orthogonal systems and approximations. Linear functionals, dual spaces, and the Riesz representaion theorem in Hilbert spaces.

Learning outcome

Improve the students knowledge in matrix methods and linear algebra, and to introduce them to basic notions and methods in linear/functional analysis.

Learning methods and activities

Lectures and mandatory exercises. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. Retake of examination may be given as an oral examination.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course is based on TMA4100/05/15/20 Calculus 1/2/3/4K, or equivalent. MA1101 Basic Calculus I, MA1102 Basic Calculus II, MA1103 Vector Calculus, MA1201 Linear Algebra and Geometry, MA1202 Linear Algebra with Applications, MA2105 Complex Function Theory with Differential Equations, or equivalent.

Course materials

Will be announced at the start of the course.

Credit reductions