430/630 LINEAR ALGEBRA II (3+0) 3 credits
Fall Semester 2006 Eric Olson
MWF 10:00-10:50AM AB 201 ejolson at unr.edu
Office hours MW 2pm and F 1pm in AB614
There will be a Final Exam on Friday Dec 16 in our
regular classroom AB201 at 9:45-11:45am.
Topics covered include all topics that have appeared
on all previous review sheets plus the following
additional material.
- The definition of generalized
eigenvectors from chapter 8 and the proofs of
Propositions 8.5 and 8.6 and Corollary 8.7.
-
Homework problems selected from the first 9 assignments
including the optional 9th assignment.
-
Know the exact statement without proof of the
- Theorem 7.9 Complex Spectral Theorem
- Theorem 7.13 Real Spectral Theorem
- Theorem 7.41 Polar Decompositions
- Theorem 7.46 Singular-Value Decomposition
- The Polarization Identity given in problems 6 and 7 of chapter 6.
- Know the characterizations of normal
operators given in 7.6, of positive operators in 7.27
and of isometries in 7.36.
- The proof of the representation Theorem 6.45.
There will be a Quiz Mon Dec 3.
Topics covered include all definition from
Chapter 7, the proofs of propositions 7.2, 7.4 and 7.6, and
the statement of the real and complex spectral theorems 7.9 and 7.13.
There will be a Quiz Wed Nov 15.
Topics covered include all definitions from
Chapter 6, proof of the triangle inequality,
use of the Gram-Schmidt procedure
to find a QR factorization of
a matrix as in problem 4 on the math 330 final,
properties of adjoints on pages 119-120 and
the proofs of Corollary 6.33 and Proposition 6.46.
There will be a Midterm on Wednesday Oct 25.
Topics covered include
- What does QED stand for at the end of a mathematical proof
and what does that mean?
- Given a matrix A find a basis for the null(A) and
range(A). This problem is essentially the same as #3 and #13
from the Math 330 final given on the first day of class.
- All definitions from Chapters 1, 2, 3 and 5 in the text.
- A section of True/False questions. If true, give
a brief justification; if false, give a counterexample.
A problem of this type is
- True of False: Let T be a linear operator on a finite
dimensional real vector space V; then there exists
a one dimensional invariant subspace W of T.
- Proofs of Theorems 2.6, 2.14, 3.4, 3.18, 5.6, 5.10 and
Propositions 1.8 and 2.8.
- Repeat of 2 homework problems from chapters 1, 2 or 3 that
have already been graded and returned.
- Additional 1 or 2 homework problems from chapters 2, 3 or 5
that have not been graded or possibly not even assigned.
There will be a Quiz on Friday Oct 20.
Topics covered include definitions
from Chapter 3 and Chapter 5,
Homework #3 and the proofs of
Theorem 5.6 and Theorem 5.10.
There will be a Quiz on Friday Sept 22.
Topics covered include defnitions
from Chapter 1 and 2 and the proofs
of Proposition 1.8, Proposition 2.8,
Theorem 2.6 and Theorem 2.14.
Last updated:
Wed Dec 13 10:50:37 PST 2006