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

Subject Matter

 * Linear Algebra
 * Tensor Theory

Contents

 * Editor's Preface


 * $1$ 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
* : Chapter $1$: Linear Spaces: $1$. Basic Concepts