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 reader to 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.