Description
Linear Algebra and Geometry, 2013
Authors: Shafarevich Igor R., Remizov Alexey O.
Language: RussianSubjects for Linear Algebra and Geometry:
Keywords
groups, rings, modules, linear algerba, matrix, projective space, vector space, matrix theory
Approximative price 49.57 €
In Print (Delivery period: 15 days).
Add to cart the book of Shafarevich Igor R., Remizov Alexey O.Publication date: 09-2014
526 p. · 15.5x23.5 cm · Paperback
Approximative price 68.56 €
In Print (Delivery period: 15 days).
Add to cart the book of Shafarevich Igor R., Remizov Alexey O.Publication date: 08-2012
526 p. · 15.5x23.5 cm · Paperback
Description
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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.
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
Clearly written and easy to read
Contains also rather deep and not trivial subjects and theorems and can also be useful for professionals
Good introduction to the subject
Numerous examples and applications of pure mathematical notions
I.R. Shafarevich is an outstanding mathematician and author of well-known books (e.g., "Basic Notions of Algebra")
Includes supplementary material: sn.pub/extras