01/11 Lecture 1. Handout. Notes. Systems of linear equations.
01/13 Lecture 2. Handout. Notes. Row operations. Echelon form.
01/15 Lecture 3. Handout. Notes. Gaussian elimination.
01/20 Lecture 4. Handout. Notes. Homogeneous systems. Reduced echelon form.
01/22 Lecture 5. Handout. Notes. Solving linear systems. Uniqueness of reduced echelon form.
01/25 Lecture 6. Handout. Notes. Kirchoff's laws.
01/27 Lecture 7. Handout. Notes. Abstract vector spaces.
01/29 Lecture 8. Handout. Notes. Spans.
02/01 Lecture 9. Handout. Notes. Linear independence.
02/03 Lecture 10. Handout. Notes. Bases.
02/05 Lecture 11. Handout. Notes. Dimension.
02/08 LECTURE CANCELLED.
02/10 Lecture 12. Handout. Notes. More on bases.
02/12 Lecture 13. Handout. Notes. Representation of vectors with respect to a basis.
02/15 Lecture 14. Handout. Notes. Row spaces and column spaces.
02/17 Lecture 15. Handout. Notes. Rank of a matrix.
02/19 Midterm 1 Review. Notes.
02/22 Lecture 16. Handout. Notes. Isomorphism.
02/24 Lecture 17. Handout. Notes. Isomorphism and dimension.
02/26 Lecture 18. Handout. Notes. Homomorphisms. Kernels and images.
03/01 Lecture 19. Handout. Notes. The rank--nullity theorem.
03/03 Lecture 20. Handout. Notes. Representation of homomorphisms with respect to bases.
03/05 Lecture 21. Handout. Notes. More on matrices of homomorphisms. The space of homomorphisms.
03/08 Lecture 22. Handout. Notes. Matrix multiplication.
03/10 Lecture 23. Handout. Notes. Matrix inverses.
03/12 Lecture 24. Handout. Notes. Computing matrix inverses.
03/15 Lecture 25. Handout. Notes. Two-sided inverses.
03/17 Lecture 26. Handout. Notes. Change-of-basis matrices.
03/19 Lecture 27. Handout. Notes. Dot products and orthogonality.
03/19 Lecture 27 addendum. Notes. Video. Gram-Schmidt orthogonalization.
03/29 Midterm 2 Review. Notes.
03/31 Lecture 28. Handout. Notes. Determinants: properties.
04/02 Lecture 29. Handout. Notes. Determinants: uniqueness.
04/05 Lecture 30. Handout. Notes. Determinants: existence.
04/07 Lecture 31. Handout. Notes. Elementary matrices.
04/09 Lecture 32. Handout. Notes. Determinants: further properties.
04/12 Lecture 33. Notes. Determinants and symmetries.
04/14 Lecture 34. Handout. Notes. Eigenvalues and eigenvectors.
04/16 Lecture 35. Handout. Notes. Similarity.
04/19 Lecture 36. Handout. Notes. Diagonalization.
04/21 Lecture 37. Handout. Notes. Jordan form.
04/23 Lecture 38. Handout. Notes. Generalized eigenspaces.
04/26 Lecture 39. Handout. Notes. Polynomials and matrices.
04/28 Lecture 40. Handout. Notes. Examples of Jordan form.
04/30 Lecture 41. Handout. Notes. Nilpotent matrices.