Linear Algebra II

Education facts

Code: MAGC07

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.

Entry requirements

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

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Linear Algebra II

  Karlstad University

  Karlstad

  Start date: 29 March 2027

  End date: 6 June 2027

  Pace of study: 50 %