Linear Algebra and Geometry - new book

Book in our database since 2012-11-27T03:41:48-05:00 (New York)
Detail page last modified on 2024-02-09T03:25:46-05:00 (New York)
ISBN/EAN: 3642309941

ISBN - alternate spelling:
3-642-30994-1, 978-3-642-30994-6
Alternate spelling and related search-keywords:
Book author: sha, remi, shafarevich igor, remizov, shafa, shafarevic
Book title: linear, linea, algebra geometry

Information from Publisher

Author: Igor R. Shafarevich; Alexey O. Remizov
Title: Linear Algebra and Geometry
Publisher: Springer; Springer Berlin
526 Pages
Publishing year: 2012-08-23
Berlin; Heidelberg; DE
Printed / Made in
Translator: David P Kramer; Lena Nekludova (Russian)
Language: English
50,28 € (DE)
51,70 € (AT)
55,50 CHF (CH)
Available
XXII, 526 p.

EA; E107; eBook; Nonbooks, PBS / Mathematik/Arithmetik, Algebra; Algebra; Verstehen; groups, rings, modules; linear algerba; matrix; projective space; vector space; matrix theory; B; Linear and Multilinear Algebras, Matrix Theory; Algebra; Geometry; Associative Rings and Algebras; Linear Algebra; Algebra; Geometry; Associative Rings and Algebras; Mathematics and Statistics; Geometrie; BB

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

From the reviews:

“Shafarevich (Russian Academy of Sciences) and Remizov (École Polytechnique, CNRS, France) provide insightful comments that apply not only to linear algebra but also to mathematics in general. … The book is quite readable … . Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals.” (J. R. Burke, Choice, Vol. 50 (8), April, 2013)

“This beautiful textbook not only reflects I. R. Shafarevich’s unrivalled mastery of mathematical teaching and expository writing, but also the didactic principles of the Russian mathematical school in teaching basic courses such as linear algebra and analytic geometry. … made accessible to a wide audience of international readers, and to further generations of students, too. … this book may be regarded as a historical document in the relevant textbook literature … .” (Werner Kleinert, Zentralblatt MATH, Vol. 1256, 2013)

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.

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