Upon completion of this course the student is able to:
- compute eigenvalues and eigenvectors of finite-dimensional linear mappings and can determine the spectral decomposition of simple linear mappings;
- determine an orthonormal basis and can determine if a mapping is self-adjoint, unitary, normal, or orthogonal.
This course code is only for repeat students who need to re-take the exam from last year.
All others: please refer to the new AM module 2 Structures and Systems 202200235 .
Linear structures II is a continuation of Linear Structures I. In this course, students continue their study of vector spaces and linear operators, by focusing on two special types of bases: Bases of eigenvectors, used in e.g. dynamical systems, and orthonormal bases used in, e.g., Fourier analysis. We briefly touch upon these applications, but the course mainly focuses on learning how to construct these bases, and proving existence conditions.