MAT 3141 (Fall 2012)

Linear Algebra II


The syllabus will be updated as the course progresses.

Date Sections of the notes Material
Sep 7 Ch. 1 Review of vector spaces
Sep 11 Ch. 2 Review of linear maps
Sep 14 Ch. 2 Review of linear maps (cont.) (Students should review Ch. 3 on their own.)
Sep 18 Ch. 4 Polynomials, linear operators and matrices
Sep 21 5.1 Divisibility in integral domains
Sep 25 5.2–5.4 Euclidean domains
Sep 28 5.4–5.6 The Unique Factorization Theorem, the Fundamental Theorem of Algebra
Oct 2 6.1–6.2 Modules, submodules
Oct 5 6.2–6.5 Submodules (cont.), free modules, direct sum of modules, module homomorphisms
Oct 9 7.1 Annihilators
Oct 12 7.2 Modules over a euclidean domain, rational canonical form
Oct 16 7.3–7.4 Primary decomposition, Jordan canonical form
Oct 19 8.1 Submodules of free modules
Oct 22–26
Study break
Oct 30 N/A Midterm exam (covers up to and including Ch. 7)
Nov 2 8.2, 8.3 The Cayley-Hamilton Theorem, submodules of free modules
Nov 6 8.4 The column module of a matrix
Nov 9 8.5, 9.1 Smith normal form, duality
Nov 13 9.1–9.2 Duality, bilinear maps
Nov 16 9.2–9.3 Bilinear maps, tensor products
Nov 20 9.4–9.5 Course evaluations. The Kronecker product, multiple tensor products
Nov 23 10.1 Review of inner product spaces
Nov 27 10.2–10.3 Orthogonal operators, adjoint operators
Nov 30 10.4 Spectral theorems
Dec 4 Notes Review

It is important to do the exercises in the lecture notes.


Below are lecture notes for the course. They are a single file that will be updated after each lecture. Please keep in mind that these are notes that the professor writes for himself when preparing the lecture and should be complemented by a student's own class notes. Often more will be said in class than is in the notes. If you notice any errors in these notes (even small typos), please inform the professor. This helps him as well as your fellow students.