Eigenvalues and eigenvectors of matrices and linear operators play an important role when
solving problems from structural mechanics and electrodynamics e.g. by describing the
resonance frequencies of systems when investigating the long-term behavior of stochastic
processes e.g. by describing invariant probability measures and as a tool for solving more
general mathematical problems e.g. by diagonalizing ordinary differential equations or
systems from control theory.This textbook presents a number of the most important numerical
methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central
ideas underlying the different algorithms and introduce the theoretical concepts required to
analyze their behavior with the goal to present an easily accessible introduction to the field
including rigorous proofs of all important results but not a complete overview of the vast
body of research. Several programming examples allow the readerto experience the behavior of
the different algorithms first-hand.The book addresses students and lecturers of mathematics
physics and engineering who are interested in the fundamental ideas of modern numerical methods
and want to learn how to apply and extend these ideas to solve new problems.
