Overview
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
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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. 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 … this book may be regarded as a historical document in the relevant textbook literature … .”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)
Authors and Affiliations
Bibliographic Information
Book Title: Linear Algebra and Geometry
Authors: Igor R. Shafarevich, Alexey O. Remizov
DOI: https://doi.org/10.1007/978-3-642-30994-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-30993-9Published: 24 August 2012
Softcover ISBN: 978-3-642-43409-9Published: 20 September 2014
eBook ISBN: 978-3-642-30994-6Published: 23 August 2012
Edition Number: 1
Number of Pages: XXII, 526
Topics: Linear and Multilinear Algebras, Matrix Theory, Algebra, Geometry, Associative Rings and Algebras