Linear Algebra and Geometry 2013th Edition by Igor R. Shafarevich (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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 … this book may be regarded as a historical document in the relevant textbook literature … .”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) From the Back Cover 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 Amazon users which were colected at the time this book was published on the website:

⭐This is a very lucid treatment on linear algebra. I used it during my first year as an undergrad to supplement my studies in linear spaces and affine geometry and found it indispensable.

⭐Great book for the Physicist. They actually explain what a determinant is, a vector space, a characteristic polynomial, and an eigen value and eigenvector are. Unfortunately, the binding on the book was defective. The “new book” was falling apart. Now I have to mail it back. I want to donate it to our library. I don’t think they would take it. Springer books have that problem often. The book was cheap both ways. BTW, there’s no geometry in it. It’s pure math- necessary math-for the applied scientist.

Keywords

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Download Linear Algebra and Geometry 2013th Edition PDF
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