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.