An Introduction to Linear Algebra and Tensors

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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: 9780486635453
  • Publisher: Dover Publications
  • Publication date: 10/18/2010
  • Series: Dover Books on Mathematics Series
  • Pages: 192
  • Product dimensions: 5.62 (w) x 8.24 (h) x 0.39 (d)

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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