# Linear Algebra II

7.5 ECTS credits

General vector spaces and linear matrices. Sum and direct sum of vector spaces. Dimension formula. Nilpotent and cyclic matrices. Tensor products of vector spaces and linear matrices. Diagonalisation of linear operators. Inner product spaces. Introduction to Hilbert spaces. Isometries. Riesz representation theorem and adjoint operators. Self-adjoint operators. Spectral theorem. Multilinear and quadratic forms. The norm of a linear operator. Positive definite and positive semidefinite operators. Sylvester's law of inertia. Generalized eigenvectors. Jordan normal form of matrix. Square roots of matrices. Minimal polynomial and Hamilton-Cayley's theorem. Matrix exponential function. Systems of linear differential equations with constant coefficients.

Students carry out a minor project individually.

Students carry out a minor project individually.

Progressive specialisation:
G2F (has at least 60 credits in first‐cycle course/s as entry requirements)

Education level:
Undergraduate level

Admission requirements:
Mathematics 60 ECTS cr of which at least 45 ECTS credits are completed, including MAGA04 Linear Algebra 7.5 ECTS cr, or equivalent.

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Mathematics Programme (studied during year 2)