Math 560: Linear Algebra
Fall 2012
Time/place: MWF 9:00–9:50 a.m. in Engineering E104
Course website: www.math.colostate.edu/∼bates/courses/F12/560
Text: Linear Algebra by Friedberg, Insel & Spence, 4th edition (ISBN 0-13-008451-4).
Instructor info: Prof. Dan Bates, bates@math.colostate.edu, Weber 221 (1-1037)
Office hours for 560: Thursday, 12-1, but please let me know beforehand if you are planning to
come in. If I am not expecting anyone, I may not be there. My schedule is extremely tight this
semester, so I have very few times when I can meet with students in my classes. If Thursday 12-1
is bad for you, try email. If that isn’t working for you, then we can try to set up a time that will
work for both of us.
Prerequisites: Basic calculus (derivatives, mostly). This is a basic graduate course in the Math
Department, so prerequisites are minimal.
Topics to be covered: See the schedule below. These are exactly the topics required by the Math
Department for this QE course.
Structure of the class: This will be a fairly standard lecture class, though I welcome your comments and ideas! Please feel free to speak up (within reason). There will be homework due most
weeks (typically on Fridays), a take-home midterm (date TBD), and a 2-hour QE final exam. The
final will be cumulative on exactly the topics listed on the QE syllabus. The unofficial rule in the
department is that everybody (other than those Math grad students beyond Part I) must take the
qualifier.
Feel free to work together on the homework, BUT you MUST turn in your own write-up! Plagiarism is entirely unacceptable. I am generally a generous grader, but I have no patience for
plagiarism and will give a 0 for the first assignment/exam on which I spot it, followed by an F for
the course for a second offense.
Grading: Each homework problem will have the same value (10 points), regardless of difficulty.
The homework will be worth 50% of your course grade. The midterm and final will each be worth
25%.
Feedback: I am always happy to hear it, even if it is negative. I am happy to adapt my teaching
style a bit if it will make the course work better for you.
Final Note: You should know that I have insulin-dependent diabetes and may therefore need to
sit down and take it easy occasionally. There is also the very slight risk that I could have very low
blood sugar at some point, causing me to pass out. If that happens (the probability of this is very
low), I will need somebody to call 911. Please don’t worry: I haven’t passed out yet and don’t
intend to! Even if I do pass out, I am not in any significant danger.
(Tentative!!!) Schedule
Date
M 8/20
W 8/22
F 8/24
M 8/27
W 8/29
F 8/31
M 9/3
W 9/5
F 9/7
M 9/10
W 9/12
F 9/14
M 9/17
W 9/19
F 9/21
M 9/24
W 9/26
F 9/28
M 10/1
W 10/3
F 10/5
M 10/8
W 10/10
F 10/12
M 10/15
W 10/17
F 10/19
M 10/22
W 10/24
F 10/26
M 10/29
W 10/31
F 11/2
M 11/5
W 11/7
F 11/9
M 11/12
W 11/14
F 11/16
M 11/19
W 11/21
F 11/23
M 11/26
W 11/28
F 11/30
M 12/3
W 12/5
F 12/7
H 12/13
Topic
syllabus, introduction to LA
vector spaces
subspaces, direct sums
linear equations, span
linear combinations, linear (in)dependence
linear (in)dependence
No class – Labor Day!
bases, dimension
linear transformations (LTs), null space, range
(same)
matrix of an LT
LT composition, matrix multiplication
invertibility
(same)
change of bases
duality
(same)
Gaussian elimination
rank, inverses
(same)
linear solving, quickly
transpose, projections, similarity
determinants
(same)
properties and Cramer’s Rule
multilinear functions
eigenvalues, eigenvectors
(same) + diagonalizability
(same)
invariant subspace, Cayley-Hamilton
generalized eigenvectors
inner products, norms, and Halloween!
(same)&Gram-Schmidt (orthogonal complements, etc.)
(same)
adjoints
normal, self-adjoint operators
orthogonal operators
projections, spectral theorem
SVD
No class - Fall Break!
No class - Fall Break!
No class - Fall Break!
QR, Schur
(same)
Jordan canonical form
normed linear spaces
(same)
Review for Final Exam
FINAL EXAM, 7:30–9:30 a.m. (yuck)
Sections (FIS, unless otherwise noted)
1.1
1.2
1.3
1.4
1.4, 1.5
1.5
1.6, Lax pp. 4–7
2.1
2.1
2.2
2.3
2.4
2.4
2.5
2.6, Lax pp. 8–13
2.6, Lax pp. 8–13
3.1
3.2
3.2
3.3,3.4
Lax pp. 21–24
4.1,4.2
4.1,.42
4.3,4.4
4.5
5.1
5.2
5.2
5.4
Lax pp. 52–56 (maybe 57–61)
6.1
6.2
6.2
6.3
6.4
6.5
6.6
6.7, Trefethen
Horn & Johnson or Trefethen
(same)
7.1,7.2
Ch. 14 of Lax
(same)