On Monday, November 21, let's have a quiz on the Courant-Fischer principle and small oscillations.

Fall-2016. Math H110 (ccn 18202): Linear Algebra

Instructor: Alexander Givental
Lectures: MWF 8-9, 310 Hearst Mining
Office hours: MWF 2-4 in 701 Evans
Textbook: Linear Algebra by Alexander Givental
This is an unpublished (and yet unfinished) textbook, which will be made freely available online. One of the previous versions of the text (which is to evolve during the semester) can be found here.

Grading policies:

Homework 30%, Quizzes 30%, Final 40%

The general idea is that you don't compete with each other. Your goal should be to learn the material as well as you can, and if all of you do really well (to which I hope very much, especially that the subject is interesting and simple) everyone will get an "A". What exactly it means to learn well will become more clear during the semester (probably after some quizzes).

Respectively, collaboration and/or use of outside sources are not prohibited but rather encouraged (exams excluded). Yet, each instance of this should be explicitly acknowledged in your work. Faulure to acknowledge one's use of somebody else's ideas is commonly known as academic plagiarism. So, start practicing the right ethics.

Weekly homework (to be posted to this website) is due on ... Wednesdays (?) in class. I strongly recommnd that you make some effort to learn bits of LaTeX, and typeset your hw. Think of how much easier it will be for the grader to read your work, and respectively how more adequate the feedback is going to be.



Chapter 1. Introduction

Chapter 2. Dramatis Personae

Chapter 3. Simple Problems

Chapter 4. Eigenvalues

Epilogue: Quivers.

Hints, answers, index


HW1, due Wed., Sep. 7: Read Sections 3 and 4 (i.e. the rest of Chapter 1)
Solve exercises: 60, 67, 68, 69, 70.

HW2, due Wed., Sep. 14.: Read: pp. 38-50 from Section "Vector Spaces"
Solve exercises: 83, 93, 97, 98, 100.

HW3, due Wed., Sep. 21: Read pages 51-71 i.e. the rest of "Vector Spaces" and "Matrices"
(I realize this is quite a bit of reading, but the thought that could console you is that only the subsection
"Bases and Dimension" has some content to it, while the rest is definitions only.)
Solve: 146, 149, 153, 156, 158.

HW4, due Wed., Sep. 28: Read pages 73-80 (on "Determinants"), and
Solve: 169, 174, 183, 188, 193.

HW5, due Wed., Oct. 5: Read pages 81-90 (to the end of Chapter 2).
Solve: 220, 224, 227b, 231, 233b.

HW6, due Wed., Oct. 12:: Read pp. 93 - 107 (Rank, Gaussian Elimination)
Solve: 235, 237, 238, 239, 241.

HW7, due Wed., Oct. 19: Read pp. 108-113 (about LPU decomposition, flags, and Bruhat cells)
Solve: 245, 250, 261, 262(e), 263(c).

HW8, due Wed., Oct. 26: Read pp. 115-126.
Solve: 266, 269, 278, 279, 280.

HW9, due Wed., Nov. 2: Read: pages 135-143 (The Spectral Theorem).
Solve: 285, 296, 301, 318, 319.

HW10, due Wed., Nov. 9: Read pp. 141-157.
Solve: 330, 339, 347, 349, 351.

HW11, due Wed., Nov. 16: Read pp. 147--162.
Solve: 367, 368, 369, 370, 372.

HW12, due Wed., Nov. 30: Read pp. 163-173.
Solve: 382, 385, 389, 394, 397(b,c,d,i,j,l)

No HW 13: We do have time for one more hw, which could be on the applications of the Jordan canonical form to dynamical systems,
but I decided instead to put here some problems from my old final exams:
For regular Math 110, without solutions, and for Math H110, with solutions. Enjoy!