Lectures on Linear Algebra

Overview

Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

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Overview

Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

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Product Details

  • ISBN-13: 9780486660820
  • Publisher: Dover Publications
  • Publication date: 9/1/1989
  • Series: Dover Books on Mathematics Series
  • Pages: 185
  • Sales rank: 819,530
  • Product dimensions: 5.50 (w) x 8.42 (h) x 0.41 (d)

Table of Contents

I. n-Dimensional Spaces. Linear and Bilinear Forms
  1. n-Dimensional vector spaces
  2. Euclidean space
  3. Orthogonal basis. Isomorphism of Euclidean spaces
  4. Bilinear and quadratic forms
  5. Reduction of a quadratic form to a sum of squares
  6. Reduction of a quadratic form by means of a triangular transformation
  7. The law of inertia
  8. Complex n-dimensional space
II. Linear Transformations
  9. Linear transformations. Operations on linear transformations
  10. Invariant subspaces. Eigenvalues and eigenvectors of a linear transformation
  11. The adjoint of a linear transformation
  12. Self-adjoint (Hermitian) transformations. Simultaneous reduction of a pair of quadratic forms to a sum of squares
  13. Unitary transformations
  14. Commutative linear transformations. Normal transformations
  15. Decomposition of a linear transformation into a product of a unitary and self-adjoint transformation
  16. Linear transformations on a real Euclidean space
  17. External properties of eigenvalues
III. The Canonical Form of an Arbitrary Linear Transformation
  18. The canonical form of a linear transformation
  19. Reduction to canonical form
  20. Elementary divisors
  21. Polynomial matrices
IV. Introduction to Tensors
  22. The dual space
  23. Tensors
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