CAAM 335 – Matrix Analysis
MWF 9:00-9:50 in Duncan Hall 1070
Instructor:
- Derek Hansen (Derek.J.Hansen |AT| rice |DOT| edu), Duncan Hall 2004, (713)348-2290
Office Hours:
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Wed & Thurs 2:00-3:30 p.m.
I will be in my office — Duncan Hall 2004 — at these times to answer any questions you have. No appointment necessary. Feel free to stop by.
Teaching Assistant:
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Jeff Hokanson (jeffreyh |AT| rice |DOT| edu), Duncan Hall 2108
Jeff's office hours: Tues 1:00-2:15
Recitation:
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Sundays, 7:30–9:00 p.m. in Duncan Hall 1075
Course Information:
- Prerequisites: MATH 212 and CAAM 210. Less formally: you should be familiar with multivariable calculus and elementary matrix manipulations (matrix addition and multiplication, Gaussian elimination), and be able to write MATLAB programs.
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Course Notes:
Matrix Analysis by Steve Cox.
Available in pdf
and as a course pack from the bookstore.
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Laboratory:
The lectures will be accompanied by an optional 1-credit
laboratory in which students examine concepts from the course more deeply
in the context of physical experiments. An interest meeting will be held during the first week of classes (Thursday evening: time and location TBA)
Link to Lab web page
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Required Work:
- Reading: Students should carefully read all of the course notes and all supplemental material posted below in the course schedule. I recommend that students try to read sections of the notes before the corresponding lecture.
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Problem Sets: Problem sets will be assigned roughly once a week. You may collaborate on the problems, but your write-up must be your own independent work. Transcribed solutions are unacceptable. You may not consult solutions from previous sections of this class.
- Late Policy: No late homework will be accepted (unless you have a good excuse, in which case you may not look at the posted solutions before you hand in the assignment).
- Exams: Three take-home exams. Each exam must be your individual, unassisted effort. Indicate compliance by writing out in full and signing the traditional pledge.
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(Tentative) Grading Scheme:
Problem Sets 40% First Exam 20% Second Exam 20% Third Exam 20%
Recommended Reading:
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Carl Meyer, Applied Matrix Analysis and Linear Algebra
Gilbert Strang, Linear Algebra and Its Applications
Gilbert Strang, Introduction to Applied Mathematics
Lars Ahlfors, Complex Analysis, 3rd ed.
R. V. Churchill and J. W. Brown, Complex Variables and Applicatons
D. J. Higham and N. J. Higham, MATLAB Guide, 2nd ed.
Getting Started with MATLAB from MathWorks
Course Schedule:
| Lecture | Date | Topics/Sections Covered | Homework Due | Additional Material |
|---|---|---|---|---|
| 1 | Mon 1/5 | Matrix-vector multiplication. Population modeling (Leslie Matrix). | lecture1.pdf, population.m | |
| 2 | Wed 1/7 | Ch. 1 (1.1–1.2) Matrix models of neurons as resistor networks. | lecture2.pdf, fib1.m | |
| 3 | Fri 1/9 | Ch. 1 (finish) Networks with resistors and batteries. | lecture3.pdf, fib2.m | |
| 4 | Mon 1/12 | Ch. 2 (2.1–2.2) 1-d mechanical systems. Gaussian Elimination. | HW1.pdf, solns1.pdf | |
| 5 | Wed 1/14 | Ch. 2 (2.2) Matrix inversion. | ||
| 6 | Fri 1/16 | Ch. 2 (2.2–2.3) Elementary row operations. LU decomposition. 2-d mechanical systems. | inverse_LU.pdf | |
| Mon 1/19 | NO CLASS TODAY (MLK Day) | |||
| 7 | Wed 1/21 | Ch.2 (2.3–2.4) 2-d mechanical systems (planar truss). | HW2.pdf, solns2.pdf | fiber.m (for Figure 2.3 of the course notes) The following should be helpful for hw3: truss.pdf, truss.m, stiff.m |
| 8 | Fri 1/23 | Ch. 3 (3.1–3.4) Range (column space) and null space. | ||
| 9 | Mon 1/26 | Ch. 3 (3.4–3.7) Basis and subspace dimension. | hw3.pdf, solns3.pdf, hw3prob2soln.m | lecture8-9.pdf, lec9.m |
| 10 | Wed 1/28 | Ch. 4 The Fundamental Theorem of Linear Algebra. | orthog_example.pdf, ftla1.m | |
| 11 | Fri 1/30 | Ch. 4 The Fundamental Theorem of Linear Algebra (cont'd). Begin Ch. 5, Least Squares. | lecture10-11.pdf | |
| 12 | Mon 2/2 | Ch. 5 (5.1–5.2) Least squares. | hw4.pdf hw4prob1.m, plotline2.m, plotline3.m, plotplane2.m, plotplane3.m solns4.pdf |
|
| 13 | Wed 2/4 | Ch. 5 (5.3) Applications of least squares. | The timed (3hrs) and untimed portions of exam 1: exam1.pdf, exam1untimed.pdf (due Fri 2/13) exam1sol.pdf, exam1untimedsol.pdf |
findfiber.m, circle.m |
| 14 | Fri 2/6 | Ch. 5 (5.4) Projections. | lab3trial.m, stiffLAB3.m, forcetable1.jpg | |
| 15 | Mon 2/9 | Ch. 5 (finish) Least squares, projections. | ||
| 16 | Wed 2/11 | Ch. 6 (6.1–6.3) Dynamical Systems, Laplace transform | arms_race.m | |
| 17 | Fri 2/13 | Ch. 6 (finish) Laplace transform, backward Euler method. | Exam 1 Due at 9 a.m. |
reaction_ode.m |
| 18 | Mon 2/16 | Ch. 7 (7.1–7.2) Complex numbers, complex functions. | hw5.pdf, hw5prob1.m solns5.pdf, vectarrow.m, hw5prob1soln.m, hw5prob3soln.m |
|
| 19 | Wed 2/18 | Ch. 7 (7.1–7.2) Complex functions, continued. | ||
| 20 | Fri 2/20 | Ch. 7 (7.2) Rational functions, partial fraction expansions | ||
| 21 | Mon 2/23 | Ch. 7 (7.3) Differentiation, the Cauchy-Riemann equations | hw6.pdf, solns6.pdf | |
| 22 | Wed 2/25 | Ch. 8 (8.1–8.2) Contour integration, Cauchy's theorem. | ||
| 23 | Fri 2/27 | Ch. 8 (8.2–8.3) Cauchy's theorem, curve replacement. | ||
| 2/28–3/7 | SPRING BREAK | |||
| 24 | Mon 3/9 | 8.3 continued. | hw7.pdf, solns7.pdf | |
| 25 | Wed 3/11 | 8.3 continued. | ||
| 26 | Fri 3/13 | Ch. 8 (8.3–8.4) The residue theorem, inverse Laplace transform. | ||
| 27 | Mon 3/16 | Finish Ch. 8 | hw8.pdf, solns8.pdf | Exam 2 posted today, due 3/25 (see below) |
| 28 | Wed 3/18 | Ch 9 (9.1) The eigenvalue problem. | ||
| 29 | Fri 3/20 | The eigenvalue problem, continued. | salmonpop_diag.m, eigenvalue_prob.pdf | |
| 30 | Mon 3/23 | Ch. 9 (9.2–9.3) The partial fraction expansion of the resolvent. | ||
| 31 | Wed 3/25 | Ch. (9.4) The spectral representation of a general square matrix. | exam2.pdf Exam 2 Due at 9 a.m.
exam2sol.pdf |
|
| 32 | Fri 3/27 | Ch. 9 (finish) The spectral representation of a general square matrix. | ||
| 33 | Mon 3/30 | Spectral decomposition: summary of facts. | hw9.pdf solns9.pdf |
|
| 34 | Wed 4/1 | Ch. 10 (10.1–10.2) The spectral representation of a symmetric matrix. | ode_example.pdf—the example I didn't finish in class (and more). Range_Pj.pdf—proof that R(P_j) is the generalized eigenspace of lambda_j. | |
| Fri 4/3 | MIDTERM RECESS | |||
| 35 | Mon 4/6 | Ch. 10 (10.3–10.4) Gram-Schmidt orthogonalization, diagonalization of symmetric matrices. | hw10.pdf, solns10.pdf | |
| 36 | Wed 4/8 | Application: internet search. | Ch. 12: Google PageRank from Cleve Moler's Experiments with MATLAB PR.m | |
| 37 | Fri 4/10 | Application: internet search, continued. | mypagerank2.m, surferRICE.m, Results for n = 6000 | |
| 38 | Mon 4/13 | Ch. 11 Singular value decomposition. | hw11.pdf, solns11.pdf | spectral_rep.pdf. This answers the question that came up during class today: when can we conclude that a representation of a square matrix is the spectral representation? |
| 39 | Wed 4/15 | Ch. 11 Singular value decomposition. Application: image compression. | svd2d.m, svd3d.m vectarrow2.m, vectarrow3.m jd.m, joedirt.jpg, wk.jpg | |
| 40 | Fri 4/17 | Ch. 11 More on the SVD. | hw12 & exam review questions | demo3.m |
| exam3.pdf Exam 3 Due at 5 p.m., Wednesday April 29
|
to contact the instructor during the first week of class, and also to contact
Disability Support Services in the Ley Student Center.