- (4/28) Hw12 is posted.
- (4/22) Hw11 is updated and preview question
10, homework solutions 9 and 10 are posted.
- (4/20) Hw 11 and the solution for p9 are
- (4/16) Preview question 9 posted.
- (4/12) Hw10, grade distribution for midterm 2
- (4/9) Preview question 8 posted.
- (4/5) Practice exam 2 solution is corrected
(prob. 2 -1/3->1/3 and -1/5-> 1/5).
Homework solution 7 and 8 are posted.
- (4/4) Practice exams and solutions are posted.
- (3/31) Hw 9 is updated.
2243 (Linear Algebra and Differential Equations)
or 2373 or 2573 (as suggested by the School of
The following knowledge is
assumed: systems of linear equations, Gaussian
elimination, determinants, vector spaces, linear
independence, basis and dimension. However I
will review these briefly.
New topics include the
Cramer's rule, the row, column spaces, linear
transformations, inner product, orthogonality,
the Gram-Schmidt algorithm, eigenvalues and
eigenvectors, diagonalization, hermitian
matrices, the singular value decomposition,
quadratic forms, positive definite matrices, the
Jordan canonical forms and some applications of
these topics. The lectures follow the text
fairly closely except those applications.
For a detailed syllabus see the Syllabus page.
- Applied Linear Algebra, by Peter J.
Olver and Chehrzad Shakiban - Book webpage (including
errata). This course basically covers
Chapters 1, 2, 3, 5, 7 and 8 of the textbook and
some applications of linear algebra.
- Instructor: Yu-jong Tzeng, Vincent
- Email: ytzeng "at" umn.edu
- Office Hours: Monday 6:10-8:00pm,
Wednesday 3:30-5pm, and by appointment.
Also feel free to ask questions by email.
Time and location
Lec 003: 12:20 PM - 01:10 PM @ Vincent Hall 211
Lec 005: 02:30 PM - 03:20 PM @ Vincent Hall 211
Grades will be based on the following percentages.
The class will be graded relative to a curve, curved
by the total final score. The curve, however, has no
“average” set in advance: a strong performance by
many students will earn a high average for the class
The grades will be recorded on moodle. Please
check your scores frequently and report to Yu-jong
ASAP if there's any error.
Preview questions are designed to give you
motivations to preview the material for the next
week on weekends. They are due on every Monday,
starting at 1/24 but the first one is only for
practice and will not be counted. Every week a link
will be posted here. You
need to login using your university ID and everyone
can only submit one answer but the answer can be
modified before the deadline. The lowest two scores
will be dropped.
There will be 5 short questions each week, and you
get 4 points for a correct answer, 3 points for an
incorrect answer and 0 points for leaving it blank.
There will be weekly homework
assignments. Homework should be turned in
class or to Yu-jong's mailbox on the first floor of
Vincent Hall. Homework is due by 4:30 pm on
Wednesdays. Late homework will not be
accepted. The lowest 2 homework grades will be
Please write legibly, never forget to put your
name and your section number on the top of your
work. Although you are encouraged to discuss
homework problems with your classmates, you have
to turn in your own work based on your own
understanding. Read the
assignments carefully. You
do not get partial credits for doing wrong
problems. Please see homework
policy for more information.
should solve the homework questions in
order; multiple sheets should be stapled together. Answers should be simplified when
possible and kept in exact form (i.e., do
not give a decimal approximation unless
There will be weekly 5-min quizzes in the beginning
of Friday classes. These problems will be similar to
homework problems. It will be designed based mainly
on material from the previous week and might be
related to material before.
The lowest 2 quiz grades will be dropped to
accommodate an absence, bad day, etc... However, if
you need to miss multiple quizzes due to a religious
observance, family emergency or academic reason, let
me know in advance.
There will be two midterm exams and a
The problems on the exams
will be similar to examples done in class and
homework problems. Please check exam
No calculators, notes and books
are allowed for any of the exams.
MIT's Linear Algebra Homepage:
http://web.mit.edu/18.06/www/ (with a variety of
resources, including the videos of Prof. Gil
Strang's lectures at MIT)
- (as a reference, MIT's book) by Professor
Gilbert Strang (email@example.com) at MIT, Introduction
to Linear Algebra (4th Ed., 2009),
Disability Accommodation: If you have, or
think you may have, a disability (e.g., mental
health, attentional, learning, chronic health,
sensory, or physical), please contact the Disability
Resource Center at 612-626-1333 to arrange
a confidential discussion regarding equitable
access and reasonable accommodations.
Please also discuss with Yu-jong early in the
semester to review how the accommodations will
be applied in the course (at least one week
before the first midterm).
- Matlab is a powerful math software to do
computations of matrices. You can get a student
Prof. Rick Moeckel's guide1
2 to use basic commands.
Policy Statements: The
University Senate statements regarding
academic dishonesty, credit, and workload
expectations, and grading standards are at: