Linear Algebra (Honours)
Instructor: Yaniv Plan
Office: 1219 Math Annex
Email: yaniv (at) math (dot) ubc (dot) ca
Lectures: MWF 10:00-11:00am, 460 CSCI.
- Wednesdays 4:00-5:00pm, 1219 Math Annex.
- Tuesdays 4:00-5:00pm, 105 Math.
Course outline, grading scheme, etc.: Outline.
Math Learning Centre. (MLC for short) A space for undergraduate students to study math together, with friendly support from tutors, who are graduate and undergraduate students in the math department. The MLC is located at LSK301 and LSK302. Every undergraduate student studying Math is welcome there! In the MLC, students may join the study groups if students wish to. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, the aim is to aid students in becoming better learners and to develop critical thinking in a mathematical setting. For additional information please visit the website.
Notes. Written by Richard Anstee. These give an intuitive approach to our material.
Different levels of generality. (Not discussed in class. Read me!)
Interchanging rows changes sign of determinant. (Technical part of proof from “Determinants”. Not discussed in class.)
Vector space, field, axioms. (Abstract definition of vector space. Missing one axiom: For every v ∈ V, there exists an element −v ∈ V, called the additive inverse of v, such that v + (−v) = 0)
Intuitive intro to abstract vector space. Subspace. Span. (Midterm covers material through this lecture.)
Vector geometry. Dot product, length, angle in high dimensions.
Reference for singular value decomposition (svd): Linear Algebra and its Applications, by D. Lay, editions 4 or 5 (but not 3). You can find it at the library among other places.
Assignment 9. Due Wednesday, April 5, at the beginning of class.
Midterm: February 17 in class. You may use a 3 inch by 5 inch index card of notes (both sides), writing utensils, but nothing else (no calculators). You can also cut out a piece of paper that is 3 inches by 5 inches.
Sample midterm. I will not post solutions, but you are welcome to ask about solutions in office hours. Note: This sample midterm does not have any abstract problems or proofs. However, our midterm may have a few abstract problems and proofs. There is a decent chance it will have a proof by induction. Possibly also a proof using only the axioms of a field or vector space.
Final exam. April 18 at 8:30am. Location: LASR 102.
I will not post solutions, but you are welcome to ask about solutions in office hours.