Book:M.A. Akivis/An Introduction to Linear Algebra & Tensors

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:

Tensor Calculus

Subject Matter

• Linear Algebra
• Tensor Theory

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

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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