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Lectures on Linear Algebraby I M Gelfand
Synopses & ReviewsPublisher Comments:Prominent Russian mathematician's concise, wellwritten exposition considers ndimensional 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 wellchosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector. Synopsis:Prominent Russian mathematician's concise, wellwritten exposition considers ndimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, introduction to tensors, and more. 1961 edition. Table of ContentsI. nDimensional Spaces. Linear and Bilinear Forms
1. nDimensional 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 ndimensional 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. Selfadjoint (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 selfadjoint 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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