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Matrix Analysis

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Matrix Analysis

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.

Linear AlgebraMathematics
Author
Steve Cox
Publisher
Rice University
Source
LibreTexts
License
CC BY
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 57 sections
  1. 01: Matrix Methods for Electrical Systems
  2. 1.01: Nerve Fibers and the Strang Quartet
  3. 1.02: Chapter 1 Exercises
  4. 02: Matrix Methods for Mechanical Systems
  5. 2.01: A Uniaxial Truss
  6. 2.02: A Small Planar Truss
  7. 2.03: The General Planar Truss
  8. 2.04: Chapter 2 Exercises
  9. 03: The Fundamental Subspaces
  10. 3.01: Column Space
  11. 3.02: Null Space
  12. 3.03: The Null and Column Spaces- An Example
  13. 3.04: Left Null Space
  14. 3.05: Row Space
  15. 3.06: Exercises- Columns and Null Spaces
  16. 3.07: Supplements - Vector Space
  17. 3.08: Supplements - Subspaces
  18. 3.09: Supplements - Row Reduced Form
  19. 04: Least Squares
  20. 4.01: Least Squares
  21. 05: Matrix Methods for Dynamical Systems
  22. 5.01: Nerve Fibers and the Dynamic Strang Quartet
  23. 5.02: The Laplace Transform
  24. 5.03: The Inverse Laplace Transform
  25. 5.04: The Backward-Euler Method
  26. 5.05: Exercises- Matrix Methods for Dynamical Systems
  27. 5.06: Supplemental - Matrix Analysis of the Branched Dendrite Nerve Fiber
  28. 06: Complex Analysis I
  29. 6.01: Complex Numbers Vectors and Matrices
  30. 6.02: Complex Functions
  31. 6.03: Complex Differentiation
  32. 6.04: Exercises- Complex Numbers Vectors and Functions
  33. 07: Complex Analysis II
  34. 7.01: Cauchy's Theorem
  35. 7.02: Cauchy's Integral Formula
  36. 7.03: The Inverse Laplace Transform- Complex Integration
  37. 7.04: Exercises- Complex Integration
  38. 08: The Eigenvalue Problem
  39. 8.01: Introduction to the Eigenvalue Problem
  40. 8.02: The Resolvent
  41. 8.03: The Partial Fraction Expansion of the Resolvent
  42. 8.04: The Spectral Representation
  43. 8.05: The Eigenvalue Problem- Examples
  44. 8.06: The Eigenvalue Problem- Exercises
  45. 09: The Symmetric Eigenvalue Problem
  46. 9.01: The Spectral Representation of a Symmetric Matrix
  47. 9.02: Gram-Schmidt Orthogonalization
  48. 9.03: The Diagonalization of a Symmetric Matrix
  49. 10: The Matrix Exponential
  50. 10.01: Overview
  51. 10.02: The Matrix Exponential as a Limit of Powers
  52. 10.03: The Matrix Exponential as a Sum of Powers
  53. 10.04: The Matrix Exponential via the Laplace Transform
  54. 10.05: The Matrix Exponential via Eigenvalues and Eigenvectors
  55. 10.06: The Mass-Spring-Damper System
  56. 11: Singular Value Decomposition
  57. 11.01: The Singular Value Decomposition