Linear Algebra and Geometry

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

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

Erscheinungsjahr:	2012
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xxii 526 S.
ISBN-13:	9783642309939
ISBN-10:	3642309933
Sprache:	Englisch
Herstellernummer:	80021514
Einband:	Gebunden
Autor:	Shafarevich, Igor R. Remizov, Alexey O.
Übersetzung:	Kramer, David P Nekludova, Lena
Hersteller:	Springer Berlin Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 35 mm
Von/Mit:	Igor R. Shafarevich (u. a.)
Erscheinungsdatum:	24.08.2012
Gewicht:	0,98 kg

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