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mathematics ph.d. student at the university of california. math110 graduate student instructor. evans hall 1095. office hours monday-thursday 2:15-3:15 pm, tuesday 9-10 am, and wednesday 6-7. |
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math110
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math110
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8/14/2008, 14:25
exam two solutions
exam two solutions are posted.
8/13/2008, 15:02 practice exam solutions
practice exam solutions are posted.
8/12/2008, 9:53 beware: false solution
my solution to 6.6.2 is false. i have given a class of marices which have square roots,
but i did not find all of them. a counterexample is the square of a 3 by 3 jordan block
associated to 0 which has jordan form consisting of one block of size 2 and one block of size 1.
i will correct my solution soon, but the description is far more complicated.
8/10/2008, 18:40 further revision on 8.3
problem 8.3.1 was revised yet again. sorry for the inconvenience. please remember you only have to do parts
1-4 of problem 8.4.
8/10/2008, 11:04 study study study guide
the final study guide is now available. use it at your own risk as i may have left out
some important information.
8/8/2008, 22:37 problem 8.3
problem 8.3 was false as written. it has been corrected.
8/8/2008, 10:49 homework 8 and notes
i have finished editing the notes (for now). exercises 8 are now available. as exercise 8.4 is super long, you only have to complete
parts 1-4. parts 5-8 are there for your own personal edification.
8/5/2008, 19:11 hints for homework 7
i have posted a few hints for homework 7. also, the course notes have been updated.
they will change frequently until about friday. i will not change them after friday except for correcting typos
for consistency in studying for the final exam.
8/4/2008, 12:30 office hours 8/4-8/6
office hours will be held 3-4 monday tuesday, and wednesday,
9-10 tuesday, and 6-7 wednesday.
7/29/2008, 17:00 rational canonical form
there was a subtle error with my definition of rational canonical form. a rational canonical form of an
operator is a matrix representation of the operator which is block diagonal where each diagonal block is the companion
matrix of a polynomial of the form p^m for a monic irreducible p dividing the minimal polynomial of T and m is a positive integer.
this error is now fixed in the notes.
7/29/2008, 16:42 walkthrough for 6.4
as problem 6.4 is very difficult, i have provided a walkthrough for the hard part of the proof.
7/26/2008, 17:05 problem 6.4
there was a problem with problem 6.4. the stipulation that min_T=p^m should have been removed. i have changed the problem on the exercises,
and i have given an extensive hint as to how to do the problem as i have changed it so late.
7/23/2008, 18:08 practice exam one
practice exam one is now available. Try to complete it
in less than or equal to one hour.
7/21/2008, 18:41 characteristic polynomial
there was an error in the definition of the characteristic polynomial, which was previously defined in the notes as det(A-zI)
for the square matrix A. the problem with this definition is that the characteristic polynomial would not be monic if A is
a square matrix of odd size. to correct this problem, the new definition of the characteristic polynomial is the standard defintion
as det(zI-A). now the polynomial is always monic. this also means that if A is the companion matrix of the polynomial p, then
the characteristic polynomial of A is p. the notes are in the process of being corrected, so do not be surprised if there are a lot
of typos (or more than usual with respect to the characteristic polynomial...). please note that this error has also been corrected in
the exercises (problem 5.3.1).
7/19/2008, 15:47 hints on homework 5
i have updated the exercises for this week by supplying a hint for 5.6. solutions for problem set 4 are posted.
7/17/2008, 14:09 solutions
solutions to the first exam have been posted. there are also some
questions that supplement
the questions given on the exam, so feel free to solve them at your own pace. also, i have posted another copy of the
exercises and solutions where the solutions are given in red after the statement of the problem.
7/07/2008, 14:09 homework 3 typos
two typos in homework three have been fixed, namely one in 3.2.2 and one in 3.3.3.
note that the parts of 3.3 have been reordered.
6/29/2008, 12:51 tentative schedule and more homework written
i have written a tentative schedule so that we can plan ahead.
also, new homework exercises have been written for the upcoming weeks.
6/28/2008, 21:16 homework due thursdays only
from now on, homework will be due on thursdays only, except for the last week, when it will be due on tuesday.
a typo was corrected on problem 2.4.3.
6/26/2008, 15:24 solutions, homework 3 changed
solutions are posted for the first problem set.
please note the changes to the third problem set.
6/24/2008, 16:04 homework 2 changed
problems 1, 2, and 3 of homework 2 have been changed. some minor typos on homework 1 were
fixed, namely in problem 1.2.2 and definition 1.1.v.
6/23/2008, 14:21 typo on homework
there was a typo in problem 1.1.a.
6/22/2008, 13:56 homework
the first few assignments are available.
each assignment is subject to change until one week prior to the due date.
6/11/2008, 11:59 syllabus and course notes
the first draft of the syllabus is now available. the syllabus is subject to change until
the end of the first week of classes. the first draft of the first few chapter of the course notes
is also available.
please use caution when accessing these notes as they are subject to editting.
5/16/2008, 16:03 linear algebra |
Last modified: 8/14/2008