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Math 115AH, Fall 2001

Honors Linear Algebra

• Official Information
• Virtual Office Hours
• Handouts
• Notes/Comments
• Linear Tranformation demo
• Eigenvector demo
• Double oscillator demo
• Multiple oscillator demo
• Proof by induction

Daily notes

• 12/12 Final grades have been posted as of about 8:30 p.m. today (Wednesday). Previous to that, I was experimenting with the MyUCLA grading scheme--I'm not sure whether those grades were visible to you as students--but if they were, they were not the ultimate grades assigned, although in most cases they were close. I used my own grading program in the end.
• 12/9 Errata:
  • In Handout BB, solution to 3(a), it should say "this becomes 1 = (-6)5"
  • Handout EE, EE-16 (d) should say eigenVECTORS.
  • Handout II, for the problem EE-16 (e) , the last row of P should be (0,0,1).
  (Thanks to E.K.)
• 12/8
  • Another problem no longer to be covered is EE-13. For the Elman final, just look for any problems that you can do, but our own final will be different in emphasis and layout--much more like our midterms.
  • Don't confuse change of basis with the matrix of a transformation relative to bases on both ends.
  • Boelter Hall 2444 is at the south end of the building.
  • In reviewing you might compare the proof of the spectral theorem for the 2 x 2 version with the proof given in lecture using induction.
• 12/7 There will be my usual office hour Monday, 1:30-2:30. Tuesday (the day of the final) and thereafter there won't be more office hours, but I'll still be around.
  Also, I do plan to add a few more comments here as people ask questions. For Virtual Office Hours, it's better to send me email so I'll notice your questions sooner; if they are of general interest I'll post my reply to you here or on VOH.
• 12/5 As mentioned in lecture, for the final exam you should know the statement of Cayley's Theorem and be able to make simple 2 by 2 examples with it, but you will not be asked for the proof of Cayley's Theorem.
  Jordan's theorem states that every square matrix is similar to a matrix in Jordan form over a field large enough to contain the eigenvalues. You should be able to state this theorem, list possible 2 by 2 forms, and do examples like the homework problems. We did not prove the theorem; the proof requires too much preparation.
  We did not prove the theorem that every permutation is even or odd but not both, so you do not need to know the proof for the exam. However, you should know the idea of even and odd permutations and be able to do problems like the homework.
  You should know how to use determinants to find the area of an ellipse or the volume of an ellipsoid, assuming you know the area of a unit circle or the volume of a unit sphere. The circle explanation has been added to the end of the posted notes for Lecture 10-W.
• 12/5 Solutions to Assignments 8-10 have been posted.
• 12/3 Old errata: Handout P, 3(b): "dependent" and "independent" need to be switched; 5(c) should have 3 + 3.
• 12/3 Change in office hours this week: Monday unchanged, 1:30-2:30. Tuesday changed to 10:30-11:30. Wednesday extra hours 1:00-2:00. Thursday no office hours. Friday extra office hour 1:00-2:00.
• 12/3 Change: All problems in Assignment #10 are not to hand in . Erratum: The due date was supposed to be Friday, Dec. 7.
• 12/2 As several people have pointed out, in Problem EE-17, the first term in the product should be (x₂ - x₁) .
• 11/27 Problem U-10 refers to Handout M. The first picture is for the identity matrix.
  In Problem Z-1, the displayed statement should say ...x < z and z < y.
• 11/26 In CC-1, L_A means tau_A. In Handout U, kernel means null space .
• 11/26 V-3 (on an earlier assignment): 100 should have been 1000.
• 11/26 V-16 Example x: When it says every two elements are related, this was intended to include having each element related to itself.
• 11/14 Since we didn't get to linear indendence of eigenvectors for distinct eigenvalues, that won't be on the midterm.
• 11/13 Notes for 3-F have been added, with the "exchange proof" of invariance of dimension.
• 11/13 In Handout V, Problem V-13, 7 goes to 1, not 4.
• 11/7 In Handout U, kernel means null space and image (which you know) is used for range.
• 11/6 On Handout R, Problem R-2: Second matrix should have e ₁ , not d ₁ .
• 11/4 On Handout Q, p. Q 4, Problem Q-7, last sentence, "not" is missing: If s is not among ...
• 10/31 Assignment 6 has been posted, but you can have until Friday Nov. 9 to do it.
• 10/30 Some people report problems running the demo program. If you're having trouble, could you let me know what software you're running? In the newest version of Windows, the Java needed is not included automatically; it's a plug-in.
  The demo should work in the PIC Lab.
• 10/23 In Handout J, J-8(b), the card numbers are A, 2, 3, 4, not A, 1, 2, 3.
• 10/22 In Handout J, J-8(b), the reference should be to G-8, not G-9.
• 10/22 Errata for problem solutions (thanks to those who pointed them out):
  p. I 9, solution to E-5 : line 3 should say t ₁ = t ₂
  p. L 1, solution to p. 15 Ex. 2 : line 4 should say 1-i/((1+i)(1-i)) = (1-i)/2 = 1/2 - 1/2 i
• 10/19 The midterm next Friday will be in Haines A18 . The second midterm will also be in a different room, to be annouced later.
• 10/18 Since the posting of Assignment 4, a small change was made in J-5(d). The printed version and the present posted version have the change.
• 10/17 Assignment 4 has been posted.
• 10/15 The full explanation of Z _p was given in the on-line notes for 1-M. I'll give the TA a printed version to pass out in section.
• 10/15 The on-line version of Handout G is now the same as the printed version passed out in class. A couple of clarifications were added to the version originally posted.
• 10/8 I have posted notes/comments for 1-F and 2-M. 1-F mentions a useful method and 2-M has suggestions on Assignment #2.
• 10/5 p. 39, Ex. 3: Should say R ⁴.
• 10/3 An erratum on Handout D: 2-(h) should say (r+s)v = rv + sv .
• 10/2 I'm changing office hours, moving Wednesday p.m. hours to Tuesday since homework is due Wednesday. So my office hours will be Mon 1:30-2:30, Tues 1:30-2:30, Thurs 2:30-3:30 , by appointment, and informally at the end of class.
• 10/1 I have posted some notes for 0-F and 1-M.
• 9/27 See also comments on some lectures under Notes/Comments . I have posted some for the first lecture 0-W (meaning week 0, Wednesday).
• 9/26 In Problem C-1, you are allowed to use the subset operations repeatedly , so it is possible to make lots of subsets.
  Also, the empty set (no elements) and the whole set both can be counted, if you can make them using these set operations.
• 9/24 Do be sure to attend the initial discussion section on Tuesday, 9/25. Our TA will give a review of some concepts from Math 33A.