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Understanding Linear Algebra

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Understanding Linear Algebra

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.

Linear AlgebraMathematics
Author
David Austin
Publisher
Grand Valley State University
Source
LibreTexts
License
CC BY
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 40 sections
  1. 01: Systems of equations
  2. 1.01: What can we expect
  3. 1.02: Finding solutions to systems of linear equations
  4. 1.03: Computation with Sage
  5. 1.04: Pivots and their influence on solution spaces
  6. 02: Vectors matrices and linear combinations
  7. 2.01: Vectors and linear combinations
  8. 2.02: Matrix multiplication and linear combinations
  9. 2.03: The span of a set of vectors
  10. 2.04: Linear independence
  11. 2.05: Matrix transformations
  12. 2.06: The geometry of matrix transformations
  13. 03: Invertibility bases and coordinate systems
  14. 3.01: Invertibility
  15. 3.02: Bases and coordinate systems
  16. 3.03: Image Compression
  17. 3.04: Determinants
  18. 3.05: Subspaces of Rp
  19. 04: Eigenvalues and eigenvectors
  20. 4.01: An introduction to eigenvalues and eigenvectors
  21. 4.02: Finding eigenvalues and eigenvectors
  22. 4.03: Diagonalization similarity and powers of a matrix
  23. 4.04: Dynamical Systems
  24. 4.05: Markov chains and Google's PageRank algorithm
  25. 05: Linear algebra and computing
  26. 5.01: Gaussian elimination revisited
  27. 5.02: Finding eigenvectors numerically
  28. 06: Orthogonality and Least Squares
  29. 6.01: The dot product
  30. 6.02: Orthogonal complements and the matrix tranpose
  31. 6.03: Orthogonal bases and projections
  32. 6.04: Finding Orthogonal Bases
  33. 6.05: Orthogonal Least Squares
  34. 07: The Spectral Theorem and singular value decompositions
  35. 7.01: Symmetric matrices and variance
  36. 7.02: Quadratic forms
  37. 7.03: Principal Component Analysis
  38. 7.04: Singular Value Decompositions
  39. 7.05: Using Singular Value Decompositions
  40. New Page