This book offers an introduction to the algorithmic-numerical thinking using basic problems of
linear algebra. By focusing on linear algebra it ensures a stronger thematic coherence than is
otherwise found in introductory lectures on numerics. The book highlights the usefulness of
matrix partitioning compared to a component view leading not only to a clearer notation and
shorter algorithms but also to significant runtime gains in 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 a bachelor's degree in mathematics.
