This book is an introduction to the algorithmic-numerical thinking by means of basic problems of linear algebra. The focus on linear algebra assures a stronger thematic coherence than it is otherwise to be found in introductory lectures on numerics. The account emphasizes the usefulness of matrix partitioning as opposed to a component view, which leads not only to a clearer notation and shorter algorithms, but also to significant runtime gains in the face of modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally - in an appendix - in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of the bachelor's degree in mathematics.

Folkmar Bornemann is Professor for Numerical Analysis and Scientific Computing at the Technical University of Munich.