Matrix Analysis

by Steve Cox

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Equilibria and the solution of linear and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration.

Description from LibreTexts.

Publisher
Rice University
Subjects
Mathematics, Linear Algebra
Licence
CC BY, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Preface to Matrix Analysis
  5. Table of Contents
  6. Licensing
  7. Preface
  8. 1: Matrix Methods for Electrical Systems
  9. 1.1: Nerve Fibers and the Strang Quartet
  10. 1.2: Chapter 1 Exercises
  11. 2: Matrix Methods for Mechanical Systems
  12. 2.1: A Uniaxial Truss
  13. 2.2: A Small Planar Truss
  14. 2.3: The General Planar Truss
  15. 2.4: Chapter 2 Exercises
  16. 3: The Fundamental Subspaces
  17. 3.1: Column Space
  18. 3.2: Null Space
  19. 3.3: The Null and Column Spaces- An Example
  20. 3.4: Left Null Space
  21. 3.5: Row Space
  22. 3.6: Exercises- Columns and Null Spaces
  23. 3.7: Supplements - Vector Space
  24. 3.8: Supplements - Subspaces
  25. 3.9: Supplements - Row Reduced Form
  26. 4: Least Squares
  27. 4.1: Least Squares
  28. 5: Matrix Methods for Dynamical Systems
  29. 5.1: Nerve Fibers and the Dynamic Strang Quartet
  30. 5.2: The Laplace Transform
  31. 5.3: The Inverse Laplace Transform
  32. 5.4: The Backward-Euler Method
  33. 5.5: Exercises- Matrix Methods for Dynamical Systems
  34. 5.6: Supplemental - Matrix Analysis of the Branched Dendrite Nerve Fiber
  35. 6: Complex Analysis I
  36. 6.1: Complex Numbers, Vectors and Matrices
  37. 6.2: Complex Functions
  38. 6.3: Complex Differentiation
  39. 6.4: Exercises- Complex Numbers, Vectors, and Functions
  40. 7: Complex Analysis II
  41. 7.1: Cauchy's Theorem
  42. 7.2: Cauchy's Integral Formula
  43. 7.3: The Inverse Laplace Transform- Complex Integration
  44. 7.4: Exercises- Complex Integration
  45. 8: The Eigenvalue Problem
  46. 8.1: Introduction to the Eigenvalue Problem
  47. 8.2: The Resolvent
  48. 8.3: The Partial Fraction Expansion of the Resolvent
  49. 8.4: The Spectral Representation
  50. 8.5: The Eigenvalue Problem- Examples
  51. 8.6: The Eigenvalue Problem- Exercises
  52. 9: The Symmetric Eigenvalue Problem
  53. 9.1: The Spectral Representation of a Symmetric Matrix
  54. 9.2: Gram-Schmidt Orthogonalization
  55. 9.3: The Diagonalization of a Symmetric Matrix
  56. 10: The Matrix Exponential
  57. 10.1: Overview
  58. 10.2: The Matrix Exponential as a Limit of Powers
  59. 10.3: The Matrix Exponential as a Sum of Powers
  60. 10.4: The Matrix Exponential via the Laplace Transform
  61. 10.5: The Matrix Exponential via Eigenvalues and Eigenvectors
  62. 10.6: The Mass-Spring-Damper System
  63. 11: Singular Value Decomposition
  64. 11.1: The Singular Value Decomposition
  65. Back Matter
  66. Index
  67. Detailed Licensing