Linear Algebra and Geometry

Authors: Shafarevich, Igor R., Remizov, Alexey

  • 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")
see more benefits

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-30994-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-3-642-30993-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-3-642-43409-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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)


Table of contents (14 chapters)

  • Linear Equations

    Shafarevich, Igor R. (et al.)

    Pages 1-23

  • Matrices and Determinants

    Shafarevich, Igor R. (et al.)

    Pages 25-77

  • Vector Spaces

    Shafarevich, Igor R. (et al.)

    Pages 79-131

  • Linear Transformations of a Vector Space to Itself

    Shafarevich, Igor R. (et al.)

    Pages 133-160

  • Jordan Normal Form

    Shafarevich, Igor R. (et al.)

    Pages 161-189

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-30994-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-3-642-30993-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-3-642-43409-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Linear Algebra and Geometry
Authors
Translated by
Nekludova, L., Kramer, D.P.
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-30994-6
DOI
10.1007/978-3-642-30994-6
Hardcover ISBN
978-3-642-30993-9
Softcover ISBN
978-3-642-43409-9
Edition Number
1
Number of Pages
XXII, 526
Topics