Handbook of linear algebra /
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| Imprint: | Boca Raton, FL : Chapman & Hall/CRC, c2007. |
|---|---|
| Description: | 1 v. (various pagings) : ill. ; 27 cm. |
| Language: | English |
| Series: | Discrete mathematics and its applications |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6168749 |
Table of Contents:
- Preliminaries
- Part I. Linear Algebra
- Basic Linear Algebra
- 1. Vectors, Matrices and Systems of Linear Equations
- 2. Linear Independence, Span, and Bases
- 3. Linear Transformations
- 4. Determinants and Eigenvalues
- 5. Inner Product Spaces, Orothogonal Projection, Least Squares and Singular Value Decomposition
- Matrices with Special Properties
- 6. Canonical Forms
- 7. Unitary Similarity, Normal Matrices and Spectral Theory
- 8. Hermitian and Positive Definite Matrices
- 9. Nonnegative and Stochastic Matrices
- 10. Partitioned Matrices
- Advanced Linear Algebra
- 11. Functions of Matrices
- 12. Quadratic, Bilinear and Sesquilinear Forms
- 13. Multilinear Algebra
- 14. Matrix Equalities and Inequalities
- 15. Matrix Perturbation Theory
- 16. Pseudospectra
- 17. Singular Values and Singular Value Inequalities
- 18. Numerical Range
- 19. Matrix Stability and Inertia
- Topics in Advanced Linear Algebra
- 20. Inverse Eigenvalue Problems
- 21. Totally Positive and Totally Nonnegative Matrices
- 22. Linear Preserver Problems
- 23. Matrices over Integral Domains
- 24. Similarity of Families of Matrices
- 25. Max-Plus Algebra
- 26. Matrices Leaving a Cone Invariant
- Part II. Combinatorial Matrix Theory and Graphs
- Matrices and Graphs
- 27. Combinatorial Matrix Theory
- 28. Matrices and Graphs
- 29. Digraphs and Matrices
- 30. Bipartite Graphs and Matrices
- Topics in Combinatorial Matrix Theory
- 31. Permanents
- 32. D-Optimal Designs
- 33. Sign Pattern Matrices
- 34. Multiplicity Lists for the Eigenvalues of Symmetric Matrices with a Given Graph
- 35. Matrix Completion Problems
- 36. Algebraic Connectivity
- Part III. Numerical Methods
- Numerical Methods for Linear Systems
- 37. Vector and Matrix Norms, Error Analysis, Efficiency and Stability
- 38. Matrix Factorizations, and Direct Solution of Linear Systems
- 39. Least Squares Solution of Linear Systems
- 40. Sparse Matrix Methods
- 41. Iterative Solution Methods for Linear Systems
- Numerical Methods for Eigenvalues
- 42. Symmetric Matrix Eigenvalue Techniques
- 43. Unsymmetric Matrix Eigenvalue Techniques
- 44. The Implicitly Restarted Arnoldi Method
- 45. Computation of the Singular Value Deconposition
- 46. Computing Eigenvalues and Singular Values to High Relative Accuracy
- Computational Linear Algebra
- 47. Fast Matrix Multiplication
- 48. Structured Matrix Computations
- 49. Large-Scale Matrix Computations
- Part IV. Applications
- Applications to Optimization
- 50. Linear Programming
- 51. Semidefinite Programming
- Applications to Probability and Statistics
- 52. Random Vectors and Linear Statistical Models
- 53. Multivariate Statistical Analysis
- 54. Markov Chains
- Applications to Analysis
- 55. Differential Equations and Stability
- 56. Dynamical Systems and Linear Algebra
- 57. Control Theory
- 58. Fourier Analysis
- Applications to Physical and Biological Sciences
- 59. Linear Algebra and Mathematical Physics
- 60. Linear Algebra in Biomolecular Modeling
- Applications to Computer Science
- 61. Coding Theory
- 62. Quantum Computation
- 63. Information Retrieval and Web Search
- 64. Signal Processing
- Applications to Geometry
- 65. Geometry
- 66. Some Applications of Matrices and Graphs in Euclidean Geometry
- Applications to Algebra
- 67. Matrix Groups
- 68. Group Representations
- 69. Nonassociative Algebras
- 70. Lie Algebras
- Part V. Computational Software
- Interactive Software for Linear Algebra
- 71. MATLAB
- 72. Linear Algebra in Maple
- 73. Mathematica
- Packages of Subroutines for Linear Algebra
- 74. BLAS
- 75. LAPACK
- 76. Use of ARPACK and EIGS
- 77. Summary of Software for Linear Algebra Freely Available on the Web
- Glossary
- Notation Index
- Index