Phu Xuan University Library
|
PXU E-LIB
Sign in
Fundamentals of Matrix Algebra

External

Fundamentals of Matrix Algebra

This text deals with matrix algebra, as opposed to linear algebra. Without arguing semantics, I view matrix algebra as a subset of linear algebra, focused primarily on basic concepts and solution techniques. There is little formal development of theory and abstract concepts are avoided. This is akin to the master carpenter teaching his apprentice how to use a hammer, saw and plane before teaching how to make a cabinet.

Linear AlgebraMathematics
Author
Gregory Hartman
Publisher
Virginia Military Institute
Source
LibreTexts
License
CC BY-NC
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 49 sections
  1. 01: Systems of Linear Equations
  2. 1.01: Introduction to Linear Equations
  3. 1.1.01: Exercises 1.1
  4. 1.02: Using Matrices to Solve Systems of Linear Equations
  5. 1.2.01: Exercises 1.2
  6. 1.03: Elementary Row Operations and Gaussian Elimination
  7. 1.3.01: Exercises 1.3
  8. 1.04: Existence and Uniqueness of Solutions
  9. 1.4.01: Exercises 1.4
  10. 1.05: Applications of Linear Systems
  11. 1.5.01: Exercises 1.5
  12. 02: Matrix Arithmetic
  13. 2.01: Matrix Addition and Scalar Multiplication
  14. 2.1.01: Exercises 2.1
  15. 2.02: Matrix Multiplication
  16. 2.2.01: Exercises 2.2
  17. 2.03: Visualizing Matrix Arithmetic in 2D
  18. 2.3.01: Exercises 2.3
  19. 2.04: Vector Solutions to Linear Systems
  20. 2.4.01: Exercises 2.4
  21. 2.05: Solving Matrix Equations AXB
  22. 2.5.01: Exercises 2.5
  23. 2.06: The Matrix Inverse
  24. 2.6.01: Exercises 2.6
  25. 2.07: Properties of the Matrix Inverse
  26. 2.7.01: Exercises 2.7
  27. 03: Operations on Matrices
  28. 3.01: The Matrix Transpose
  29. 3.1.01: Exercises 3.1
  30. 3.02: The Matrix Trace
  31. 3.2.1: Exercises 3.2
  32. 3.03: The Determinant
  33. 3.3.1: Exercises 3.3
  34. 3.04: Properties of the Determinant
  35. 3.4.1: Exercises 3.4
  36. 3.05: Cramer's Rule
  37. 3.5.1: Exercises 3.5
  38. 04: Eigenvalues and Eigenvectors
  39. 4.01: Eigenvalues and Eigenvectors
  40. 4.1.1: Exercises 4.1
  41. 4.02: Properties of Eigenvalues and Eigenvectors
  42. 4.2.1: Exercises 4.2
  43. 05: Graphical Explorations of Vectors
  44. 5.01: Transformations of the Cartesian Plane
  45. 5.1.1: Exercises 5.1
  46. 5.02: Properties of Linear Transformations
  47. 5.2.1: Exercises 5.2
  48. 5.03: Visualizing Vectors- Vectors in Three Dimensions
  49. 5.3.1: Exercises 5.3