Linear Algebra and Its Applications, 2nd Edition

Preface to the First Edition.

1. Fundamentals.

2. Duality.

3. Linear Mappings.

4. Matrices.

5. Determinant and Trace.

6. Spectral Theory.

7. Euclidean Structure.

8. Spectral Theory of Self-Adjoint Mappings.

9. Calculus of Vector- and Matrix-Valued Functions.

10. Matrix Inequalities.

11. Kinematics and Dynamics.

12. Convexity.

13. The Duality Theorem.

14. Normed Linear Spaces.

15. Linear Mappings Between Normed Linear Spaces.

16. Positive Matrices.

17. How to Solve Systems of Linear Equations.

18. How to Calculate the Eigenvalues of Self-Adjoint Matrices.

19. Solutions.

Bibliography.

Appendix 1. Special Determinants.

Appendix 2. The Pfaffian.

Appendix 3. Symplectic Matrices.

Appendix 4. Tensor Product.

Appendix 5. Lattices.

Appendix 6. Fast Matrix Multiplication.

Appendix 7. Gershgorin's Theorem.

Appendix 8. The Multiplicity of Eigenvalues.

Appendix 9. The Fast Fourier Transform.

Appendix 10. The Spectral Radius.

Appendix 11. The Lorentz Group.

Appendix 12. Compactness of the Unit Ball.

Appendix 13. A Characterization of Commutators.

Appendix 14. Liapunov's Theorem.

Appendix 15. The Jordan Canonical Form.

Appendix 16. Numerical Range.

Index.