Linear Algebra (MATH 511, Fall 2017)

Teacher: Alexandre Eremenko
OFFICE HOURS: Math 600 Tuesday 3:00-4:00 + by appointment

PHONE: (765) 494-1975

EMAIL: eremenko@math.purdue.edu

GENERAL INFORMATION

Notice: We use FOURTH edition of Strang's text Linear Algebra and its applicatons. The Homework is assigned from the 4-th edition. It must be available in the University bookstore, and there is a copy on reserve in the MATH library on the 3-d floor of the Math building.

HW 1 (due August 29, before the class begins) 1.2.5, 1.2.11, 1.2.13, 1.3.1, 1.3.4, 1.3.5, 1.4.1, 1.4.14, 1.4.17, 1.4.19.

HW 2: (due September 5) 1.5.4, 1.5.11, 1.5.14, 1.5.15, 1.6.6, 1.6.10, 1.6.11, 2.1.2, 2.1.7, 2.2.3, 2.2.6.

HW 3 (due September 12): 2.3.2, 2.3.7, 2.3.10, 2.3.13, 2.3.20, 2.4.3, 2.4.18, 2.4.20, 2.6.1, 2.6.6, 2.6.8, 2.6.9, 2.6.16.

HW 4 (due September 19): 2.6.18, 2.6.19, 2.6.21, 3.1.2, 3.1.6, 3.1.9, 3.1.16, 3.2.3, 3.2.5, 3.2.8, 3.2.9, 3.2.10.

HW 5 (due September 26): 3.3.4, 3.3.6, 3.3.12, 3.3.18, 3.4.6, 3.4.13, 3.4.14, 3.4.20, 3.4.21, 3.4.28.

Midterm exam is on Thursday, October 5, in class. It is an exam with closed books, no notes or calculators are allowed. Covers chapters 1,2,3, except 1.7, 2.5, 3.5. The problems in the exam will be similar to those in HW and in Review sections at the end of each chapter. Some problems are with full credit, and others yes/no or multiple choice type. There will be a review on October 3.

HW 6 (due October 3) is in the handout here, all exercises WITHOUT star(*): pdf. In addition to this handout you may read "Complex numbers and their conjugates" on p. 281-282, and from "Complex roots of Unity" to "Fast Fourier transform" on p. 189-193. This material is not covered by the midterm exam.

Here you can see pictures of an analog Fourier synthesizer, a high-precision instrument, used to compute Fourier coefficients and to sum a Fourier series in pre-computer era (until the middle of XX century).
And here is a short biography of Cornelius Lanczos who invented the Fast Fourier transform while working at Purdue University.

Exam solutions

HW 7 (due Oct. 24): 4.2.3, 4.2.4, 4.2.5, 4.2.17, 4.3.7, 4.3.8, 4.3.12, 4.3.13, 4.4.3, 4.4.13, 4.4.14, 4.4.24.

You may find this handout: Determinants useful (There are no problems in it, it is just a condensed exposition of the topic).

HW 8 (due Oct. 31): 5.1.1, 5.1.5, 5.1.7, 5.1.14, 5.1.18, 5.2.1, 5.2.2, 5.2.5, 5.2.6, 5.2.9, 5.2.10, 5.2.15.

Additional topics: Spectral theorems for Hermitian and unitary matrices (required reading), 25 billion dollars eigenvector (optional reading).

HW 9 (due Nov. 7): 5.3.4, 5.3.6, 5.3.9, 5.4.1, 5.4.8, 5.4.9, 5.4.14, 5.4.15, 5.5.7, 5.5.12, 5.5.17, 5.5.20.

HW 10 (due Nov. 14): 5.6.2, 5.6.14, 5.6.15, 5.6.16 (a) 5.6.23, 5.6.24, 5.6.28, 5.6.30, 5.6.31,

HW 11 (due Nov. 21) 6.1.2, 6.1.7, 6.1.13. 6.2.1, 6.2.7, 6.2.10, 6.2.12, 6.2.15.

Singular Value Decomposition.

HW 12 (due Nov. 28, last one): 6.3.5, 6.3.2, 6.3.11, 6.3.12, 6.4.1, 6.4.5, 6.4.7, 6.4.11 (Read p. 339-341 for 6.4.1).