Linear Algebra and Geometry

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...

Full description

Bibliographic Details
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:
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-30994-6
LEADER 03053nam a22004815i 4500
001 14784
003 DE-He213
005 20130727034944.0
007 cr nn 008mamaa
008 120823s2013 gw | s |||| 0|eng d
020 # # |a 9783642309946  |9 978-3-642-30994-6 
024 7 # |a 10.1007/978-3-642-30994-6  |2 doi 
050 # 4 |a QA184-205 
072 # 7 |a PBF  |2 bicssc 
072 # 7 |a MAT002050  |2 bisacsh 
082 0 4 |a 512.5  |2 23 
100 1 # |a Shafarevich, Igor R.  |e author. 
245 1 0 |a Linear Algebra and Geometry  |c by Igor R. Shafarevich, Alexey O. Remizov.  |h [electronic resource] / 
264 # 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2013. 
300 # # |a XXI, 526 p. 70 illus.  |b online resource. 
336 # # |a text  |b txt  |2 rdacontent 
337 # # |a computer  |b c  |2 rdamedia 
338 # # |a online resource  |b cr  |2 rdacarrier 
347 # # |a text file  |b PDF  |2 rda 
505 0 # |a 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. 
520 # # |a 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. 
650 # 0 |a Mathematics. 
650 # 0 |a Algebra. 
650 # 0 |a Matrix theory. 
650 # 0 |a Geometry. 
650 1 4 |a Mathematics. 
650 2 4 |a Linear and Multilinear Algebras, Matrix Theory. 
650 2 4 |a Algebra. 
650 2 4 |a Geometry. 
650 2 4 |a Associative Rings and Algebras. 
700 1 # |a Remizov, Alexey O.  |e author. 
710 2 # |a SpringerLink (Online service) 
773 0 # |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783642309939 
856 4 0 |u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-30994-6 
912 # # |a ZDB-2-SMA 
950 # # |a Mathematics and Statistics (Springer-11649)