Linear Algebra and Geometry

Igor R. Shafarevich, Alexey O. Remizov, David P Kramer , Lena Nekludova

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Russian

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
20 September 2014

Mathematics & Sciences; Algebra; Geometry

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.

By: Igor R. Shafarevich, Alexey O. Remizov
Translated by: David P Kramer, Lena Nekludova
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Dimensions: Height: 235mm, Width: 155mm, Spine: 28mm
Weight: 831g
ISBN: 9783642434099
ISBN 10: 3642434096
Pages: 526
Publication Date: 20 September 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Linear Algebra and Geometry

From the reviews: Shafarevich (Russian Academy of Sciences) and Remizov (Ecole 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)