Linear algebra and geometry

The book is a course of linear algebra and geometry, based on lectures, which for many years have been read by one of the authors at the Mechanics and Mathematics Faculty of Moscow State University.
The presentation of the subject begins with the theory of linear equations and matrices and is then conducted in the language of vector spaces. The book also describes the theory of affine and projective spaces. In addition, some topics are included, naturally adjacent to linear algebra, but usually in such courses are not considered: external algebras, geometry of Lobachevsky, topological properties of projective spaces, theory of quadric in multidimensional affine and projective spaces, decomposition of finite abelian groups and finite-born periodic modules ( Similar the theorem on the Jordan normal form of linear transformation) The presentation is accompanied by examples illustrating the use of the theory under study. Its relations with other sections of mathematics, including the theory of differential equations, differential geometry and mechanics are considered.
The book is designed for students and teachers of mathematical and physical and mathematics.
Recommended by the Scientific and Methodological Council on Mathematics of the Ministry of Education and Science of the Russian Federation as a textbook for students of higher educational institutions, students in the direction 0101 - "Mathematics" and 0107 - "Physics"