Reading: Shastri: Section 2.1 (just skim through the basic concepts and facts).
Exercises: Shastri, 2nd edition: Exercise 1.9.5 (what Shastri means by Gram-Schmidt is also known as the QR decomposition), 1.9.10, 1.9.23, 2.1.10 (iv), 2.1.17, Remark 2.1.22 (1, 8). Note that the second definition of an extreme point of a convex set in the textbook, the one given in parentheses after the definition of a face, Definition 2.1.12, has to be corrected to "implies x = y or x = z." Use these definitions for arbitrary convex sets. For polytopes, it is equivalent to the half-space definition I gave in class on Wednesday.
Suggestion: I believe working in study groups and consulting the hints is beneficial to learning things neither is cheating. But give the problem a thought before discussing it with friends or consulting the hints section.
Warning: If you use the 1st edition of the textbook, check the assigned exercises against the 2nd edition copy available online through the Library, as the numbering has changed between the two editions!
Last modified: (2019-09-27 15:09:52 CDT)