Understanding Linear Algebra

by David Austin

Read here Read at LibreTextsPDF

This book arises from my belief that linear algebra, as presented in a traditional undergraduate curriculum, has for too long lived in the shadow of calculus. Many mathematics programs currently require their students to complete at least three semesters of calculus, but only one semester of linear algebra, which often has two semesters of calculus as a prerequisite.

Description from LibreTexts.

Publisher
Grand Valley State University
Subjects
Mathematics, Linear Algebra
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. About the Book
  6. Licensing
  7. 1: Systems of equations
  8. 1.1: What can we expect
  9. 1.2: Finding solutions to systems of linear equations
  10. 1.3: Computation with Sage
  11. 1.4: Pivots and their influence on solution spaces
  12. 2: Vectors, matrices, and linear combinations
  13. 2.1: Vectors and Linear Combinations
  14. 2.2: Matrix multiplication and linear combinations
  15. 2.3: The span of a set of vectors
  16. 2.4: Linear independence
  17. 2.5: Matrix transformations
  18. 2.6: The geometry of matrix transformations
  19. 3: Invertibility, bases, and coordinate systems
  20. 3.1: Invertibility
  21. 3.2: Bases and coordinate systems
  22. 3.3: Image Compression
  23. 3.4: Determinants
  24. 3.5: Subspaces of Rp
  25. 4: Eigenvalues and Eigenvectors
  26. 4.1: An introduction to Eigenvalues and Eigenvectors
  27. 4.2: Finding eigenvalues and eigenvectors
  28. 4.3: Diagonalization, similarity, and powers of a matrix
  29. 4.4: Dynamical Systems
  30. 4.5: Markov chains and Google's PageRank algorithm
  31. 5: Linear Algebra and Computing
  32. 5.1: Gaussian Elimination Revisited
  33. 5.2: Finding Eigenvectors Numerically
  34. 6: Orthogonality and Least Squares
  35. 6.1: The Dot Product
  36. 6.2: Orthogonal Complements and the Matrix Tranpose
  37. 6.3: Orthogonal bases and projections
  38. 6.4: Finding Orthogonal Bases
  39. 6.5: Orthogonal Least Squares
  40. 7: The Spectral Theorem and singular value decompositions
  41. 7.1: Symmetric matrices and variance
  42. 7.2: Quadratic forms
  43. 7.3: Principal Component Analysis
  44. 7.4: Singular Value Decompositions
  45. 7.5: Using Singular Value Decompositions
  46. 8: Appendix A Sage Reference
  47. Back Matter
  48. Index
  49. Glossary
  50. Detailed Licensing