Essence of Linear Algebra

Introductory Mathematics by Cheetahs. 14 lectures, 2.4 hours. Covers: visual intuition linear transformations matrices determinant eigenvectors.

Lectures

  1. Vectors | Chapter 1, Essence of linear algebra · 10 min
  2. Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra · 10 min
  3. Linear transformations and matrices | Chapter 3, Essence of linear algebra · 11 min
  4. Matrix multiplication as composition | Chapter 4, Essence of linear algebra · 10 min
  5. Three-dimensional linear transformations | Chapter 5, Essence of linear algebra · 5 min
  6. The determinant | Chapter 6, Essence of linear algebra · 10 min
  7. Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra · 12 min
  8. Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra · 4 min
  9. Dot products and duality | Chapter 9, Essence of linear algebra · 14 min
  10. Cross products | Chapter 10, Essence of linear algebra · 9 min
  11. Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra · 13 min
  12. Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra · 12 min
  13. Change of basis | Chapter 13, Essence of linear algebra · 13 min
  14. A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra · 13 min

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