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Dover Books on Mathematics Ser.: Introduction to Linear Algebra and Tensors by M. A. Akivis and V. V. Goldberg (2010, Trade Paperback)
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About this product
Product Identifiers
PublisherDover Publications, Incorporated
ISBN-100486635457
ISBN-139780486635453
eBay Product ID (ePID)963550
Product Key Features
Number of Pages192 Pages
Publication NameIntroduction to Linear Algebra and Tensors
LanguageEnglish
Publication Year2010
SubjectAlgebra / Linear
TypeTextbook
AuthorM. A. Akivis, V. V. Goldberg
Subject AreaMathematics
SeriesDover Books on Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Height0.4 in
Item Weight8 Oz
Item Length8.2 in
Item Width5.6 in
Additional Product Features
Intended AudienceCollege Audience
LCCN77-078589
Dewey Edition19
TitleLeadingAn
IllustratedYes
Dewey Decimal512.5
Edition DescriptionReprint,Revised edition,New Edition
Table Of ContentEditor's Preface Chapter 1. Linear Spaces 1. Basic Concepts 2. Linear Dependence 3. Dimension and Bases 4. Orthonormal Bases. The Scalar Product 5. The Vector Product. Triple Products 6. Basis Transformations. Tensor Calculus 7. Topics in Analytic Geometry Chapter 2. Multilinear Forms and Tensors 8. Linear Forms 9. Bilinear Forms 10. Multilinear Forms. General Definition of a Tensor 11. Algebraic Operations on Tensors 12. Symmetric and Antisymmetric Tensors Chapter 3. Linear Transformations 13. Basic Concepts 14. The Matrix of a Linear Transformation and Its Determinant 15. Linear Transformations and Bilinear Forms 16. Multiplication of Linear Transformations and Matrices 17. Inverse Transformations and Matrices 18. The Group of Linear Transformations and Its Subgroups Chapter 4. Further Topics 19. Eigenvectors and Eigenvalues 20. The Case of Distinct Eigenvalues 21. Matrix Polynomials and the Hamilton-Cayley Theorem 22. Eigenvectors of a Symmetric Transformation 23. Diagonalization of a Symmetric Transformation 24. Reduction of a Quadratic Form to Canonical Form 25. Representation of a Nonsingular Transformation Selected Hints and Answers; Bibliography; Index
SynopsisThe present book, a valuable addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics. A special merit of the book is its free use of tensor notation, in particular the Einstein summation convention. The treatment is virtually self-contained. In fact, the mathematical background assumed on the part of the reader hardly exceeds a smattering of calculus and a casual acquaintance with determinants. The authors begin with linear spaces, starting with basic concepts and ending with topics in analytic geometry. They then treat multilinear forms and tensors (linear and bilinear forms, general definition of a tensor, algebraic operations on tensors, symmetric and antisymmetric tensors, etc.), and linear transformation (again basic concepts, the matrix and multiplication of linear transformations, inverse transformations and matrices, groups and subgroups, etc.). The last chapter deals with further topics in the field: eigenvectors and eigenvalues, matrix ploynomials and the Hamilton-Cayley theorem, reduction of a quadratic form to canonical form, representation of a nonsingular transformation, and more. Each individual section -- there are 25 in all -- contains a problem set, making a total of over 250 problems, all carefully selected and matched. Hints and answers to most of the problems can be found at the end of the book. Dr. Silverman has revised the text and numerous pedagogical and mathematical improvements, and restyled the language so that it is even more readable. With its clear exposition, many relevant and interesting problems, ample illustrations, index and bibliography, this book will be useful in the classroom or for self-study as an excellent introduction to the important subjects of linear algebra and tensors., Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition., Lucid, eminently readable work: linear spaces, linear transformations, matrix polynomials, etc. Silverman translation. 250 problems., Eminently readable and completely elementary, this treatment begins with linear spaces and ends with analytic geometry. Additional topics include multilinear forms, tensors, linear transformation, eigenvectors and eigenvalues, matrix polynomials, and more. More than 250 carefully chosen problems appear throughout the book, most with hints and answers. 1972 edition.
LC Classification NumberQA184.A391
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