Understanding the topics from basic linear algebra, as listed below.

Lecture

MatricesSystems of linear equationsVector spaces and subspacesBasis and dimensionInvertible matricesLinear mappingsDeterminantsEigenvalues and eigenvectorsDiagonalizationInner product spacesEigenvalues of symmetric matrices

High school mathematics

None

Lecture summaries (published on moodle).Seymour Lipschutz. Schaum's Outline of Linear Algebra. (German version: Lineare Algebra. Theorie und Anwendung.)Link auf weitere Informationenhttps://www.google.com/

The grade will be solely determined by the final exam.It will be a closed book exam (Prüfung ohne Unterlagen/Hilfsmittel). In particular, books, written or printed notes, calculators, etc.,  will not be permitted.Dates for the exam:3 July 2025,22 July 2025,30 September 2025.More exam dates will be offered during the Winter Semester (tentatively, in November 2025 and in January 2026).Every student can take any of these exams, and, if needed, retake it without any restriction, as long as the number of available attempts (Prüfungsantritte) allows that. (NB: Different rules apply to the exercise course!)

The final exam will consist of both theoretical and method-based questions. Theoretical questions will assess knowledge and understanding of definitions, key results, and their proofs. Method-based questions will evaluate the mastery of the methods learned throughout the course. 

The maximum possible score (P) for the exam will be 20 points. This score will be converted into the final grade for the course as follows:P < 12  →  5 (failing the course)12 ≤ P < 14  →  414 ≤ P < 16  →  316 ≤ P < 18  →  218 ≤ P ≤ 20  →  1