Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).
In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.
Voila, IOP with some solns. [I've typed solns for the key parts of each problem, but not for the routine parts.].
In (X1), the IP problem, you will now see a boldface, red 6. I had intended the lower-left entry in matrix G3 to be 6, but accidentally typed a 0. When you read the soln-sheet, just substitute 0 for 6 in both the question and the answer.
Part (X2d) asks for four KxK matrices A,B,C,D, where Det of block-matrix [ A B ] [ C D ] fails-to-equal Det(AD - CB). It is insufficient to produce non-commuting A and C. You need to produce also B and D, and to compute that the determinants are unequal. Indeed, it is possible to have non-commuting A and C, and still have equality of the determinants.
Nifty-cool (X4), Dim(Span(Perm-matrices)),
can be done quickly with Hall's Marriage Lemma, which itself has a quick proof.
Nonetheless, I decided to do a bare-hands sand shifting
proof, written
in exquisite detail. A textbook would write it in 5 sentences. I chose to
split it into several tiny lemmas, so it takes a whole page. Note
that it produces an algorithm for writing
a given constant-row/column-sum matrix as a lin.comb of permutation matrices;
a fun programming challenge for the programmers among you.
Pamphlet Differentiating a bilinear function (pdf) shows how to generalize the Product Rule to other bilinear functions.
Least Squares and matrices (pdf): Derivation of a formula for Least-squares fitting of a line to data points (also has HW problems). Available are two examples of a more-general curve-fitting formula (txt).
Have read the beginning of Characteristic_polynomial. The defn we'll use is in Cayley-Hamilton pamphlet (pdf)
We will also discuss the statement Jordan Canonical Form (JCF), In particular, I would like you to know the stmt and proof of the Block Upper-Triangular--matrix Lemma [just page 4 in JCF].
The delightful Class-V (pdf) is now online.
Work through Determinant (W). In progress is Properties of Determinants.
Please read the first few paragraphs of: Bilinear_map and Bilinear_form, as well as Multilinear_map and Alternating_multilinear_map.
This demo page illustrates these linear transformations: Dilations, Rotations and Shears. It also shows the affine transformation of Translation.
Please peruse the Wikipedia pages that define Group, Ring, Field as well as Set builder notation.
Quantifiers ∀ and ∃ (“for all” and “there exists”) are like nitroglycerin, in that one little mis-step leads to the whole thing blowing up in your face.
There is no partial credit when it comes to Explosives and Quantifiers.
-JLF King
Our LinA class has a LISTSERV archive. I will email to each student how to post-to and read-from the Archive. (The archive is at a private URL, only for the use of the folks in our class.)
Author: | Friedberg, Insel, Spence | ISBN: | 978-0134860244 |
Year: | 2019 | Publisher: | Pearson |
Webpages: Lina, 2016g and Lina, 2015t and Lina, 2011t and Lina, 2010t [the latter also has Lina, 2005], as well as Computational Linear Algebra from 2007 [Spring & Aut.], Spring2002 and Autumn1998. All of my previous courses' “Notes, Exams and Links” are available from the Teaching Page.
...is due, slid u n d e r my office door (Little Hall 402, Northeast corner) no later than 1PM, Thursday, 21Apr2022.
This IOP (pdf), must be carefully typed, but diagrams may be hand-drawn.
At all times have a paper copy you can hand-in; I do
NOT accept
electronic versions.
Print out a copy each day, so that you always have the latest version to
hand-in; this, in case your printer or computer fails.
(You are too old for My dog ate my homework.
)
Please follow the guidelines on the Checklist (pdf, 3pages) to earn full credit.