Linear Algebra and Its Applications, 2e + Functional Analysis Set

Linear Algebra and Its Applications, 2nd Edition

Preface.

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.

Functional Analysis

Foreword.

Linear Spaces.

Linear Maps.

The Hahn-Banach Theorem.

Applications of the Hahn-Banach Theorem.

Normed Linear Spaces.

Hilbert Space.

Applications of Hilbert Space Results.

Duals of Normed Linear Space.

Applications of Duality.

Weak Convergence.

Applications of Weak Convergence.

The Weak and Weak* Topologies.

Locally Convex Topologies and the Krein-Milman Theorem.

Examples of Convex Sets and their Extreme Points.

Bounded Linear Maps.

Examples of Bounded Linear Maps.

Banach Algebras and their Elementary Spectral Theory.

Gelfand's Theory of Commutative Banach Algebras.

Applications of Gelfand's Theory of Commutative Banach Algebras.

Examples of Operators and their Spectra.

Compact Maps.

Examples of Compact Operators.

Positive Compact Operators.

Fredholm's Theory of Integral Equations.

Invariant Subspaces.

Harmonic Analysis on a Halfline.

Index Theory.

Compact Symmetric Operators in Hilbert Space.

Examples of Compact Symmetric Operators.

Trace Class and Trace Formula.

Spectral Theory of Symmetric, Normal and Unitary Operators.

Spectral Theory of Self-Adjoint Operators.

Examples of Self-Adjoint Operators.

Semigroups of Operators.

Groups of Unitary Operators.

Examples of Strongly Continuous Semigroups.

Scattering Theory.

A Theorem of Beurling.

Appendix A: The Riesz-Kakutani Representation Theorem.

Appendix B: Theory of Distributions.

Appendix C: Zorn's Lemma.

Author Index.

Subject Index.