Book:M.A. Akivis/An Introduction to Linear Algebra & Tensors
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M.A. Akivis and V.V. Goldberg: An Introduction to Linear Algebra & Tensors
Published $\text {1972}$, Dover Publications
- ISBN 0-486-63545-7 (translated by Richard A. Silverman)
Translated from:
Subject Matter
Contents
- Editor's Preface (Richard A. Silverman)
- $1$ LINEAR SPACES
- 1. Basic Concepts
- 2. Linear Dependence
- 3. Dimension and Bases
- 4. Orthonormal Bases. The Scalar Product
- 5. The Vector Product. Triple Products
- 6. Basis Transformations. Tensor Calculus
- 7. Topics in Analytic Geometry
- $2$ MULTILINEAR FORMS AND TENSORS
- 8. Linear Forms
- 9. Bilinear Forms
- 10. Multilinear Forms. General Definition of a Tensor
- 11. Algebraic Operations on Tensors
- 12. Symmetric and Asymmetric Tensors
- $3$ LINEAR TRANSFORMATIONS
- 13. Basic Concepts
- 14. The Matrix of a Linear Transformation and Its Determinant
- 15. Linear Transformations and Bilinear Forms
- 16. Multiplication of Linear Transformations and Matrices
- 17. Inverse Transformations and Matrices
- 18. The Group of Linear Transformations and Its Subgroups
- $4$ FURTHER TOPICS
- 19. Eigenvectors and Eigenvalues
- 20. The Case of Distinct Eigenvalues
- 21. Matrix Polynomials and the Hamilton-Cayley Theorem
- 22. Eigenvectors of a Symmetric Transformation
- 23. Diagonalization of a Symmetric Transformation
- 24. Reduction of a Quadratic Form to Canonical Form
- 25. Representation of a Nonsingular Transformation
- Selected Hints and Answers
- Bibliography
- Index
Source work progress
- 1972: M.A. Akivis and V.V. Goldberg: An Introduction to Linear Algebra & Tensors (translated by Richard A. Silverman) ... (previous) ... (next): Chapter $1$: Linear Spaces: $1$. Basic Concepts