The 2019 Linear Algebra Workshop was offered as part of the PI4 program, and was be led by Elliot Kaplan, building on materials developed in previous years by Stef Klajbor Goderich. The goal of the workshop is to review and learn some advanced linear algebra with an eye towards applications and the Computational Bootcamp, which runs immediately after this workshop.

What is the format of the workshop?
Students work in groups through the worksheets (see files below). Informal presentations and discussions on the most important problems occur throughout the day. The style is informal, with students working in a collaborative environment.

How are the worksheets structured?
Each day’s worksheet contains a list of definitions, theorems, and exercises (about 40 each day). Some of the problems were modified from those in the references, while others are problems written for this working group.

  • Day 1 Worksheet    (Day1_Sheet)
    Projections and the Gram-Schmidt Process
    QR Factorization
    Linear Models: Regression
  • Day 2 Worksheet    (Day2_Sheet)
    Symmetric matrices
    Spectral Theorem
    Quadratic Forms
    Singular Value Decomposition
  • Day 3 Worksheet    (Day3_Sheet)
    Principal Component Analysis and Dimensional Reduction
    Brief look at Markov Chains
    LU Factorizations
    Duals and annihilators
    Some multilinear algebra

These Linear Algebra Workshop materials may be freely used by others. We ask that when materials are re-used, the following statement be included:

These materials were created by Stefan Klajbor Goderich at the University of Illinois and edited by Elliot Kaplan, with support from National Science Foundation grant DMS 1345032 “MCTP: PI4: Program for Interdisciplinary and Industrial Internships at Illinois.”