Linear Algebra and Geometry

• Main Authors: Shafarevich, Igor R. (Author), Remizov, Alexey O. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Subjects: Mathematics.; Algebra.; Matrix theory.; Geometry.; Linear and Multilinear Algebras, Matrix Theory.; Associative Rings and Algebras.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-30994-6

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, inn...

Table of Contents:

• 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.