Linear Algebra and Its Applications

Peter D. Lax (Autor)

Software / Digital Media

320 Seiten

2007 | 2nd Edition
John Wiley & Sons Inc (Hersteller)
9780470178751 (ISBN)

Infos

Gives an introduction to linear algebra with an emphasis on the analytical aspects of the subject as well as its applications. This book discusses linear equations, matrices, determinants, and vector spaces. It also includes a number of topics, such as eigenvalues, the Hahn Banach theorem, geometry, game theory, and numerical analysis.

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This introduction to linear algebra by world renowned mathematician Peter Lax is unique in its emphasis on the analytical aspects of the subject as well as its numerous applications. The book grew out of Dr. Lax's course notes for the linear algebra classes he taught at New York University. Geared to graduate students as well as advanced undergraduates, it assumes only limited knowledge of linear algebra and avoids subjects already heavily treated in other textbooks. While it discusses linear equations, matrices, determinants, and vector spaces, it also includes a number of exciting topics, such as eigenvalues, the Hahn Banach theorem, geometry, game theory, and numerical analysis.

Inhalt

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 of a Euclidean Space into Itself.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 of Selected Exercises.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.List of Series Titles.

Produkt-Details

• Erscheint lt. Verlag: 11.3.2008
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-13: 9780470178751 / 9780470178751
• Zustand: Neuware