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Lectures on Linear Algebra

Publisher: 
Dover Publications
Number of Pages: 
185
Price: 
10.95
ISBN: 
0486660826
Date Received: 
Monday, August 21, 2006
Reviewable: 
Yes
Include In BLL Rating: 
Yes
I. M. Gel'fand
Publication Date: 
1989
Format: 
Paperback
Category: 
Textbook
BLL
07/14/2009
BLL Rating: 

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
Publish Book: 
Modify Date: 
Tuesday, July 14, 2009

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