Lectures on Linear Algebra

Lectures on Linear Algebra

4.63 (11 ratings by Goodreads)
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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

  • Paperback | 185 pages
  • 138 x 214 x 10mm | 223g
  • New York, United States
  • English
  • New edition
  • New edition
  • 0486660826
  • 9780486660820
  • 78,221

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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