Linear algebra (Osnabrück 2024-2025)/Part I
This is the English version of the material (lecture notes, exercises) of a mathematical course taught at the University of Osnabrück. So this is not an online course, only the material for a real university course. The material is organized in a modular way (e.g., facts, proofs, examples, and exercises are in separate files) so that it can also be used in other courses. The mathematical material is quite standard for a university beginners class, and the course has been taught several times. The English version is a direct translation. Suggestions are welcome.
Linear algebra is a fundamental course in mathematics. It deals with "linear structures“: linear systems of equations, vectors and their representation, bases and base change, linear mappings and matrices, determinants, eigenvalues and eigenvectors, optimal descriptions of linear mappings, affine mappings, normed vector spaces, lengths and angles, analytic geometry, isometries and symmetries, bilinear forms, more general algebraic structures like equivalence relations, groups, residue class construction, and multilinear algebra.