Overview


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.
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An Introduction to Linear Algebra and Tensors

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Overview


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.
Read More Show Less

Product Details

  • ISBN-13: 9780486148786
  • Publisher: Dover Publications
  • Publication date: 6/27/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 192
  • File size: 6 MB

Table of Contents

Editor'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
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