Linear algebra — original English

Original English mathematics by Jim Hefferon, from Linear Algebra.

34 linked sections through Complex Vector Spaces, not the complete book. The original explanations, proofs, exercises and supplied answers are preserved. Separate source notes explain specific findings without silently changing the original mathematics.

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  1. Linear Systems — 57 exercises with supplied answers
  2. Linear Geometry — 42 exercises with supplied answers
  3. Reduced Echelon Form — 31 exercises with supplied answers
  4. Computer Algebra Systems — 4 exercises with supplied answers
  5. Input-Output Analysis — 4 exercises with supplied answers
  6. Accuracy of Computations — 5 exercises with supplied answers
  7. Analyzing Networks — 5 exercises with supplied answers
  8. Vector Spaces — 59 exercises with supplied answers
  9. Linear Independence — 26 exercises with supplied answers
  10. Basis and Dimension — 100 exercises with supplied answers
  11. Fields — 5 exercises with supplied answers
  12. Crystals — 4 exercises with supplied answers
  13. Voting Paradoxes — 6 exercises with supplied answers
  14. Dimensional Analysis — 6 exercises with supplied answers
  15. Maps Between Spaces — 48 exercises with supplied answers
  16. Homomorphisms — 54 exercises with supplied answers
  17. Computing Linear Maps — 45 exercises with supplied answers
  18. Matrix Operations — 89 exercises with supplied answers
  19. Change of Basis — 40 exercises with supplied answers
  20. Projection — 55 exercises with supplied answers
  21. Line of Best Fit — 9 exercises with supplied answers
  22. Geometry of Linear Maps — 7 exercises with supplied answers
  23. Magic Squares — 5 exercises with supplied answers
  24. Markov Chains — 7 exercises with supplied answers
  25. Orthonormal Matrices — 5 exercises with supplied answers
  26. Determinants — 73 exercises with supplied answers
  27. Geometry of Determinants — 24 exercises with supplied answers
  28. Laplace’s Formula — 19 exercises with supplied answers
  29. Cramer’s Rule — 8 exercises with supplied answers
  30. Speed of Calculating Determinants — 5 exercises with supplied answers
  31. Chiò’s Method — 4 exercises with supplied answers
  32. Projective Geometry — 7 exercises with supplied answers
  33. Computer Graphics — 5 exercises with supplied answers
  34. Complex Vector Spaces — 0 exercises with supplied answers

Extending a linearly independent set to a basis — read the preceding independence, exchange and dimension arguments as needed. This link is not certification of another course’s proof dependencies.

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