About this book
Introduction
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, nonEuclidean 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.
Keywords
Bibliographic information
 Book Title Linear Algebra and Geometry

Authors
Igor R. Shafarevich
Alexey O. Remizov
 DOI https://doi.org/10.1007/9783642309946
 Copyright Information SpringerVerlag Berlin Heidelberg 2013
 Publisher Name Springer, Berlin, Heidelberg
 eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
 Hardcover ISBN 9783642309939
 Softcover ISBN 9783642434099
 eBook ISBN 9783642309946
 Edition Number 1
 Number of Pages XXII, 526
 Number of Illustrations 0 b/w illustrations, 0 illustrations in colour

Topics
Linear and Multilinear Algebras, Matrix Theory
Algebra
Geometry
Associative Rings and Algebras
 Buy this book on publisher's site
 Industry Sectors
 Finance, Business & Banking
Reviews
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. Upperdivision 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)