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Linear Algebra and Geometry

Linear Algebra and Geometry - 12 edition

Linear Algebra and Geometry - 12 edition

ISBN13: 9783642309939

ISBN10: 3642309933

Linear Algebra and Geometry by SHAFAREVICH IG - ISBN 9783642309939
Edition: 12
Copyright: 2012
Publisher: Springer-Verlag New York, LLC
Published:
International: No
Linear Algebra and Geometry by SHAFAREVICH IG - ISBN 9783642309939

ISBN13: 9783642309939

ISBN10: 3642309933

Edition: 12

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Summary

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.