Class Diary for M251, Fall 2003, Jochen Denzler
Wed Aug 20: Intro; systems of lin eqns
Fri Aug 22: systems of lin eqns (sec 1.1, 1.2); matrix multiplication.
Hwk 1-16 due Fri; Hwk: pdf file
Hwk: dvi file
Mon Aug 25: 0 is a *trivial* solution of a *homogeneous* system
(vocabulary) Transpose; trace; zero & identity matrices;
matrix multiplication; read sec 1.2, 1.3.
Wed Aug 27: basic rules of matrix algebra; inverse of a matrix;
calculation by simultaneous solution of systems of linear eqns.
Fri Aug 29: Hwk 17-24 due next Friday: see page 3 of the (now updated)
old hwk file: Hwk: pdf file
Hwk: dvi file. Inverse of a matrix;
elementary matrices. Essentially, we have covered all the way
through 1.5 now. Reread this material in book.
Note updated glossary: glossary: pdf file
glossary: dvi file (available as of 5pm)
Mon Sep 01: LABOR DAY
---> Solutions to Hwk 1-16 available here
Wed Sep 03: Sec 1.6: Theoretical results concerning invertible matrices
Fri Sep 05: Sec 1.6; Sec 1.7: triangular, diagonal, symmetric matrices,
their products and inverses
---> Solutions to Hwk 17-24 available here
Mon Sep 08: LU decomposition: its purpose and how to find it. New Hwk:
numbers 25-31, due Friday:
Hwk: pdf file
Hwk: dvi file (cumulative file; see page 4)
---> Glossary has been updated with pages 6 and 7:
glossary: pdf file
glossary: dvi file
Wed Sep 10: Vectors in R2 and R3
New homework: number 32 due either Friday or Monday (as you prefer).
Study according to number 33 by Monday, for quiz.
Hwk: pdf file
Hwk: dvi file (cumulative file; see page 5)
Special office hour Friday after class, or by appointment, if you
have questions like ``what do they actually ask in the
problems listed as hwk 33?''
Fri Sep 12: Discussed hwk 30, 31; Norm of geometric vectors;
dot (scalar) product defined.
---> Solutions to Hwk 24-32 available here
by Friday or Monday, as applicable.
Mon Sep 15:
---> Glossary has been updated:
glossary: pdf file
glossary: dvi file
Wed Sep 17: Dot Product; Projections; quick preview of cross product
Fri Sep 19: FIRST IN-CLASS EXAM; Covers Ch.~1 (incl 9.9),
Sec's 3.1-3.3
---> Solutions now available
Mon Sep 22: Discussion of exam; cross product geometrically,
and in coordinates. Homework due Monday
Hwk: pdf file
Hwk: dvi file
---> Glossary has been updated:
glossary: pdf file
glossary: dvi file
Wed Sep 24: (Note that the hwk from last time has increased and
is now all due on Monday only). Cross product, area, 2x2 determinants;
scalar triple product, volume and 3x3 determinants
Fri Sep 26: Determinants; definition via permutations; row- and column
transformations (sec 2.1, 2.2)
Mon Sep 29 : more properties of determinants. Homework due next Monday
Hwk: pdf file
Hwk: dvi file
---> Solutions to Hwk Ch 3
Wed Oct 01: Minors, cofactors, cofactor expansion, adjoint matrix.
Formula for A-1; Cramer's rule (no proofs; facts and examples
only)
Fri Oct 03: One example on determinants; n-space. The previous sheet
of homeworks (Hwk: pdf file
Hwk: dvi file) has been updated
with four more problems: These are due next Friday.
---> Glossary has been updated (1 1/2 more pages):
glossary: pdf file
glossary: dvi file
Mon Oct 06: linear functions
Rn -> Rn. New homework due
Friday, if at all possible (pblm 1-6):
Hwk: pdf file
Blank hwk sheet with corrdinate grid for convenience download: pdf
(same as ps file here)
---> Solutions to Hwk Ch 2, pblms 1-11
Wed Oct 08: Examples of linear transformations: Rotations and
reflections
in R3. Eigenvectors and eigenvalues. More Hwk
problems handed out already: you can start now; they will be due
later.
---> Glossary has been updated (6 more pages):
glossary: pdf file
glossary: dvi file (page 22 posted
already, but not handed out yet, as it contains future material)
Fri Oct 10: Discussion of Hwk pblm 14: adj(adj(A)).
How to calculate eigenvalues and eigenvectors.
New hwk; pblms 7-11 due Mon Oct 20; review
pblms 12-15 due Oct 24 (same as ps file)
---> Solutions to Hwk Ch 2, pblms 12-15
(scroll down)
---> Solutions to Hwk Ch 4, Pblms 1-6 (pdf format):
A, B,
C, D,
E, F.
Same in ps format:
A, B,
C, D,
E, F.
(Available Monday)
Mon Oct 13: Vector spaces
Wed Oct 15: Subspaces; linear comb's; span
Fri Oct 17: FALL BREAK
---> Solutions to Hwk Ch 4, pblms 7-11
Mon Oct 20: Linear (in)dependence
Wed Oct 22: Basis of a vector space
Fri Oct 24: EXAM 2
Mon Oct 27: Basis of a vector space.
New Homework, due next Monday
---> Glossary has been updated (2 more pages):
glossary: pdf file
glossary: dvi file
Wed Oct 29: Basis; coordinate vectors; row space, column space,
null space
Fri Oct 31: Discussion of Exam 2; review of material based on
common mistakes therein
Mon Nov 03: Instead of a lecture: Guided hwk on row, column,
null space.
New Homework, due next Monday: pblms 11-20 ;
Pblms 21-23 due Friday Nov 14 (but there will be more for Nov 14)
---> Solutions to Hwk Ch 5, pblms 1-10
---> Solutions to Pingpong Hwk
---> Solutions to Exam 2
Wed Nov 05: Inner product spaces
Fri Nov 07: Discussion Hwk; quick review:
rank, nullity, dimension formula; Proof of Cauchy-Schwarz inequality
New Homework, due next Friday: pblms 1-9 ;
---> Glossary has been updated (4 more pages):
glossary: pdf file
glossary: dvi file
Mon Nov 10: Orthogonal complements
---> Solutions to Hwk Ch 5, pblms 11-20
(scroll down in file to find them)
Wed Nov 12: Repetition, questions, what'll be on the exam;
Projections;
---> 4 more hwk pblms added: not due Friday, but required to prepare
for exam. We'll discuss Monday whether you prefer to turn them in for grade
by Wed 19 or by Fri 21, or whether we just won't grade them.
Fri Nov 14: Gram Schmidt orthogonalization
Mon Nov 17: Eigenvalues; geometric and algebraic multiplicity
---> Solutions to Hwk Ch 6, pblms 1-13
Wed Nov 19: Review, questions, and evaluation
Fri Nov 21: EXAM 3
---> Hwk for Ch 7 We won't grade it;
I'll post solutions
---> The glossary has been updated (36 pages total; that's it):
glossary: pdf file
glossary: dvi file
Mon Nov 24: Eigenvalues and Diagonalization
Wed Nov 26: Diagonalization thm for symmetric matrices;
Rmks on Exam 3
Fri Nov 28: THANKSGIVING BREAK
---> Sol's for Exam3
---> Sol's for Hwk 7 (available by Monday)
Mon Dec 01: Review
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Wed Dec 03: STUDY DAY
Thu Dec 04: EXAM DAY
Fri Dec 05: STUDY DAY
M251: class meets: MWF 1:25-2:15 ==> exam is Wed Dec 10, 2:45- 4:45