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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Shafarevich, Igor R. (Autor), Remizov, Alexey O. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Temas:
Algebras, Linear.
Algebra.
Geometry.
Associative rings.
Associative algebras.
Linear Algebra.
Associative Rings and Algebras.
Acceso en línea:Texto Completo

MARC

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100 1 |a Shafarevich, Igor R.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Linear Algebra and Geometry  |h [electronic resource] /  |c by Igor R. Shafarevich, Alexey O. Remizov. 
250 |a 1st ed. 2013. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2013. 
300 |a XXII, 526 p.  |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 Algebras, Linear. 
650 0 |a Algebra. 
650 0 |a Geometry. 
650 0 |a Associative rings. 
650 0 |a Associative algebras. 
650 1 4 |a Linear Algebra. 
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.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783642309953 
776 0 8 |i Printed edition:  |z 9783642434099 
776 0 8 |i Printed edition:  |z 9783642309939 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-642-30994-6  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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