Linear Algebra and Analytic Geometry: Linear Mappings, Matrices, Determinants, Eigenvalue Theory, and Euclidean and Unitary Vector Spaces

This textbook offers a clear and systematic introduction to linear algebra and analytic geometry at university level. It covers the central topics of the early university curriculum, including vector spaces, linear transformations, matrices, determinants, eigenvalue theory, and Euclidean and unitary vector spaces. The mathematical theory is developed with precision and in a logically structured way, with all major results fully proved. At the same time, the clear didactic presentation ensures that even demanding content remains accessible and easy to follow. Numerous examples, exercises, and fully worked solutions support understanding, promote effective exam preparation, and make the book well suited for independent study. It is ideal for students of mathematics, computer science, physics, engineering, and related fields.