Cover Image

Handbook of linear algebra /

Show other versions (3)

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the front...

Full description

Bibliographic Details
Corporate Author: Taylor & Francis
Other Authors: Hogben, Leslie (Editor)
Format: eBook
Language:English
Published: Boca Raton, Florida : Chapman and Hall/CRC, [2013]
Edition:Second edition.
Series:Discrete mathematics and its applications ; 82.
Subjects:
Algebras, Linear.
Algèbre linéaire.
Algebras, Linear
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Front Cover; Dedication; Acknowledgments; The Editor; Contributors; Contents; Preface; Preliminaries; I. Linear Algebra; 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, Orthogonal Projection, Least Squares, and Singular Value Decomposition; 6. Canonical Forms for Similarity; 7. Other Canonical Forms; 8. Unitary Similarity, Normal Matrices, and Spectral Theory; 9. Hermitian and Positive Definite Matrices.
  • 10. Nonnegative Matrices and Stochastic Matrices11. Partitioned Matrices; Topics in Linear Algebra; 12. Schur Complements; 13. Quadratic, Bilinear, and Sesquilinear Forms; 14. Multilinear Algebra; 15. Tensors and Hypermatrices; 16. Matrix Equalities and Inequalities; 17. Functions of Matrices; 18. Matrix Polynomials; 19. Matrix Equations; 20. Invariant Subspaces; 21. Matrix Perturbation Theory; 22. Special Types of Matrices; 23. Pseudospectra; 24. Singular Values and Singular Value Inequalities; 25. Numerical Range; 26. Matrix Stability and Inertia; 27. Generalized Inverses of Matrices.
  • 28. Inverse Eigenvalue Problems29. Totally Positive and Totally Nonnegative Matrices; 30. Linear Preserver Problems; 31. Matrices over Finite Fields; 32. Matrices over Integral Domains; 33. Similarity of Families of Matrices; 34. Representations of Quivers and Mixed Graphs; 35. Max-Plus Algebra; 36. Matrices Leaving a Cone Invariant; 37. Spectral Sets; II. Combinatorial Matrix Theory and Graphs; Combinatorial Matrix Theory; 38. Combinatorial Matrix Theory; 39. Matrices and Graphs; 40. Digraphs and Matrices; 41. Bipartite Graphs and Matrices; 42. Sign Pattern Matrices.
  • Topics in Combinatorial Matrix Theory43. Permanents; 44. D-Optimal Matrices; 45. Tournaments; 46. Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs; 47. Spectral Graph Theory; 48. Algebraic Connectivity; 49. Matrix Completion Problems; III. Numerical Methods; Numerical Methods for Linear Systems; 50. Vector and Matrix Norms, Error Analysis, Efficiency, and Stability; 51. Matrix Factorizations and Direct Solution of Linear Systems; 52. Least Squares Solution of Linear Systems; 53. Sparse Matrix Methods; 54. Iterative Solution Methods for Linear Systems.
  • Numerical Methods for Eigenvalues55. Symmetric Matrix Eigenvalue Techniques; 56. Unsymmetric Matrix Eigenvalue Techniques; 57. The Implicitly Restarted Arnoldi Method; 58. Computation of the Singular Value Decomposition; 59. Computing Eigenvalues and Singular Values to High Relative Accuracy; 60. Nonlinear Eigenvalue Problems; Topics in Numerical Linear Algebra; 61. Fast Matrix Multiplication; 62. Fast Algorithms for Structured Matrix Computations; 63. Structured Eigenvalue Problems
  • Structure-Preserving Algorithms, Structured Error Analysis; 64. Large-Scale Matrix Computations.