The last homework set, due Dec 2, is now posted on
the website.  It was also written on the blackboard
in class this morning.


New item:

PRESENTATIONS OF PROOFS:

I think we can benefit from some critical discussions
of proofs.

So, for EXTRA CREDIT, I'm inviting each member of the
class to pick one or more Lemmas, or Theorems, and
prepare to present any of them at the blackboard in class
on Nov 30.  Any theorem or problem in the relevant
portions of the book, Chapters 1 through 7, is
acceptable.  KEEP IT SHORT.  Let's impose an arbitrary
limit of 8 lines; if you can't prove the assertion in
that length, then please shrink it by assuming stronger
hypotheses or a weaker conclusion.

I'll then lead a critical discussion in which we all
try to find bugs in each others' presentations.

Please EMAIL me your selection a.s.a.p.  As overlapping
requests are likely,  I'll follow a policy approximating
"first requested, first granted" policy.  So enter your
requests a.s.a.p.  Probably your best strategy is to
request one theorem immediately, followed  5 or 10 minutes
later by another email containing a second request in
case the first one has already been claimed.

An ideal presentation should take less than 5 minutes.
If we do 8 such on Nov 30, each followed by 5 minutes
of discussion, we'll consume the full 1 hour 20 minute
period.

Depending on how things go on Nov 30, overflow requests
may be deferred to my office hour that afternoon,
or possibly to the last class on Dec 2.


Elwyn Berlekamp


Assignments will be annexed below:

===========================================================
COMPLETED on Tues Nov 30:

mkarsh@uclink4.berkeley.edu 
 If N is nilpotent, then N has only an eigenvalue of 0,
 and it cannot be symmetric.

sarating@uclink4.berkeley.edu
Pg 158: 3.3-3N

vtham@angelfire.com 
Pg 167: 3Q 

ilai@uclink4.berkeley.edu
Pg 254: 5C
nxn matrix A has n linearly independent eigenvectors Then if these vectors
are chosen to be the Columns of a Matrix S, it follows that S^(-1)AS is a
diagonal matrix Lambda, with the eignenvalues of A along its diagonal:

byu@hkn.eecs.berkeley.edu
Quiz 3, problem 4.6 (part of Perron's Theorem)

guyb@uclink4.berkeley.edu
Pg 141: 3F

dwhitm@excite.com 
Pg 304-305: 5P

reeber@cory.EECS.Berkeley.EDU 
Pg 251: 5B, "Trace"
 +
Pg 251: 5B, "Determinant", (if time permits)

==================================================================
DEFERRED til Thursday Dec 2:

huynhvan@uclink4.berkeley.edu
Pg 308: 5R


horie@cory.EECS.Berkeley.EDU
Pg 302: If A is Hermition then A +iI is invertible

==================================================================
SCHEDULED for first presentation on Thursday Dec 2:

roman_a@uclink4.berkeley.edu
Pg 259: 5F   or

onavarre@hotmail.com
Pg 256: 5D

Jemynigh@aol.com (Andrew Bundy)
Pg 86: 2K and 2L


StevenC95@aol.com 
A product AB of invertible matrices has an inverse.  It is found by 
multiplying the individual inverses in reverse order:
(AB)^-1 = (B^-1)(A^-1)


melyi@hotmail.com 
If the columns of a square matrix are orthonormal then the rows of that 
matrix are also orthonormal.