•     Review material: Complex numbers - appendix B and supplementary material
• Lecture 1; from the supplementary material, try 10.1 #3 b), 4 e), f), 5, 8, 10, 13, 16; 10.2 #4, 6
• Lecture 2; from the supplementary material, 10.2, #5, 7, 9, 11, 18, 23; 10.3 #5, 7, 15

•     Chapter 4 - 5: Review of vector spaces and introduction to complex vector spaces
• Lecture 3; section 4.1, #3 - 11, 27
• Lecture 4; section 4.2, #9 - 13, 16, 17; section 4.3, #3 - 5, 11, 24 - 27
• Lecture 5; section 4.4, #5, 9, 14, 25, 26; section 4.5, #9, 17, 11, 22

•     Chapter 5: sections 5.1, 5.2, review of eigenvalues and eigenvectors; chapter 6, inner product spaces
• Lecture 6; section 5.3, 15 - 18
• Lecture 7; section 5.1, #9, 11, 13, 17, 25; section 5.2, #5, 7, 17, 27

•     Chapter 6; inner product spaces, sections  6.1, 6.2, cont'd
• Lecture 8; section 6.1 #4, 10, 11, 14, 30, 31, 43, 44
• Lecture 9; section 6.2, #3, 11, 13, 17, 21, 23, 35, 39 (very important example; we will eventually do this one in class but take a shot at this; remember trig substitutions), 41
• Lecture 10 will just use the slides from Lecture 9
  

•      Sections 6.2 - 6.3
• Lecture 11
• Lecture 12; section 6.3, #3, 4, 7, 10, 11, 14
• Lecture 13; section 6.3, #21, 23, 31, 41, 42, 43, 53

Week 6, Oct. 7 - 11; first test on Oct. 9; no class on Oct. 11

• Lecture 14 section 6.4, #3, 7, 17, 24

•     section 6.4, Fourier series, Linear transformations, section 8.1
• Lecture 15 section 6.6, #2, 8
• Lecture 16 (I used these slides in lecture 15 to explain the integral calculations.)
• Lecture 17 section 8.1, #1, 7, 10, 11, 19, 21, 25, 27, 31, 33

•     Sections 8.2 - 8.3
• Lecture 18 section 8.2, #1, 3, 7, 17, 19, 21, 29, 31
• Lecture 19 section 8.3, #3, 5, 9, 15, 21
• No new slides for Friday
  

•     Sections 8.4 - 8.5
  
• Lecture 21
• Lecture 22; section 8.4, #1, 5, 13, 17, 21, 23

•     Chapter 7, orthogonal diagonalization, section 7.1 - 7.2, 7.5
• Lecture 23; section 8.5, #5, 9, 15, 21, 25, 27
  
• Lecture 24; section 7.1, #7, 12, 21, 22, 26, 30 (this one might take some work but explains what is going on in 3 dimensions)
• We will use the slides from Lecture 24; section 7.2, #11, 12, 17, 19, 21, 26, 29

•     Normal and hermitian diagonalization, section 7.3 - 7.5
• Lecture 26; section 7.5, #7, 11, 13, 17, 39, 41
• Lecture 27
• We will use the slides from Lecture 27
  

•     Optimization of quadratic forms and canonical forms, section 7.4; section 9.4
• Lecture 28 section 7.3, #2, 5, 8, 13, 15
• Lecture 29 section 7.4, #3, 5, 7, 13, 15, 21
• Dec. 2 slides are contained in Lecture 29
• Final lecture slides; the theorems on SVD are from lecture 29, the theorem of Tao et al is here and here is the SVD example.
• References: Here is a link to the article by Tao; the blog post by Andrew Gibiansky (nice hat) and the book on Deep Learning by Goodfellow, Bengio and Courville - check out chapter 2.