Lectures on Linear Algebra

Gel'fand, I. M.

ISBN 10: 0486660826 / ISBN 13: 9780486660820

Editore: Dover Publications, New York, NY, 1989

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185 pp. Tightly bound. Spine not compromised Text is free of markings. No ownership markings.

Codice articolo 024870

Dati bibliografici

• Titolo: Lectures on Linear Algebra
• Editore: Dover Publications, New York, NY
• Data di pubblicazione: 1989
• Lingua: Inglese
• ISBN 10: 0486660826
• ISBN 13: 9780486660820
• Rilegatura: Paperback
• Condizione: Near Fine
• Cataloghi dei venditori:
  • Dover

Descrizione articolo

Riassunto

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.

Contenuti

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