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Lectures on Linear Algebra

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Lectures on Linear Algebra Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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, introduction to tensors, and more. 1961 edition.

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

Product Details

ISBN:
9780486660820
Translator:
Shenitzer, A.
Author:
Shenitzer, A.
Author:
Gelfand, I. M.
Author:
fand
Author:
Mathematics
Author:
’
Author:
fand, I. M.
Author:
gel
Author:
I. M. Gel
Publisher:
Dover Publications
Location:
New York :
Subject:
Calculus
Subject:
Algebra - General
Subject:
Algebra - Linear
Subject:
Algebras, linear
Subject:
General Mathematics
Subject:
Mathematics-Calculus
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
2420
Publication Date:
19890931
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
185
Dimensions:
8.5 x 5.38 in 0.48 lb

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Related Subjects


Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Differential Equations

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Product details 185 pages Dover Publications - English 9780486660820 Reviews:
"Synopsis" by ,
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, introduction to tensors, and more. 1961 edition.

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