//]]>
Normal View MARC View ISBD View

Linear Algebra and Geometry

by Shafarevich, Igor R.
Authors: Remizov, Alexey O.%author. | SpringerLink (Online service) Physical details: XXI, 526 p. 70 illus. online resource. ISBN: 3642309941 Subject(s): Mathematics. | Algebra. | Matrix theory. | Geometry. | Mathematics. | Linear and Multilinear Algebras, Matrix Theory. | Algebra. | Geometry. | Associative Rings and Algebras.
Tags from this library:
No tags from this library for this title.
Item type Location Call Number Status Date Due
E-Book E-Book AUM Main Library 512.5 (Browse Shelf) Not for loan

Preface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index.

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

There are no comments for this item.

Log in to your account to post a comment.