Lineare Algebra

This textbook, in its updated new edition, provides a clear approach to the topic of linear algebra, unlike any other implementation. The theory is initially developed for the plane and the visual space. Due to the geometric background, the significance of the statements and their proofs can be much more easily understood. This greatly facilitates the entry into the general theory of vector spaces, linear mappings, determinants, etc. The material is presented clearly and compactly on the left side, while the corresponding exercises for deepening understanding are on the right side. Since it is impossible to learn the abstract theory of linear algebra without solving a sufficient number of standard problems, there is an abundance of such tasks. The theory is supplemented with many programming exercises in Sagemath, a computer algebra system based on Python. Solutions to the exercises can be found on the Companion Website. This book provides a modern and pedagogically appealing presentation of classical linear algebra for the first two semesters. It is aimed at students of mathematics and physics and is also particularly well-suited for students training to become teachers in these subjects. An ideal preparation for exams.