Jay Pantone

Assistant Professor
Marquette University


MSSC 6040

Fall 2019, Marquette University

The main theme of this course is foundational linear algebra considered from a numerical viewpoint. We focus on solutions of linear systems of equations, eigenvalues and eigenvectors, and transformations. The course emphasizes and illustrates proof and numerical implementation using problems arising in applications. Multivariable calculus and linear algebra are prerequisites.

  • Lectures:
    M, W 2:00pm - 3:15pm
    Cudahy 120
  • Office Hours:
    Monday, 3:45pm - 5:00pm
    Cudahy 307 Tuesday, 2:00pm - 3:30pm
    Friday, 11:00am - 12:00pm
    and by appointment

Course Information

The official syllabus is here.



LaTeX Resources

I recommend using Overleaf (free) to write your assignments in LaTeX. You can use this document as a basic template by cloning it to your own account.


I'm happy to help troubleshoot your LaTeX in office hours!

Matlab Installation

Important Dates
Aug 26 Classes begin
Sept 2 Labor Day, no classes
Sept 3 Last day to add/drop classes or request CR/NC option
Oct 10-16 Midterm exams
Oct 17-20 Midterm break, no classes
Nov 15 Last day to withdraw from classes
Nov 27 - Dec 1 Thanksgiving break, no classes
Dec 7 Last day of classes
Dec 9 Math 2100/2350 final exam

Daily Calendar
# Date Topics Homework
& Announcements
1 Mon, Aug 26 Syllabus
Lecture 1: Linear Algebra Review
2 Wed, Aug 28 Lecture 1: Linear Algebra Review
Mon, Sept 2 Labor Day — no class
3 Wed, Sept 4 Lecture 1: Linear Algebra Review Homework 1
Due Wednesday, September 11, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 1.3
Suggested Extra Problems (not collected):
  • T-B: 1.1, 1.2ab, 1.4
4 Mon, Sept 9 Lecture 2: Orthogonal Vectors and Matrices No homework today.
5 Wed, Sept 11 Finish Lecture 2
Lecture 3: Norms
Homework 2
Due Wednesday, September 18, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 2.1
Suggested Extra Problems (not collected):
  • T-B: 2.3, 2.4
6 Mon, Sept 16 Finish Lecture 3
Lecture 4: Singular Value Decomposition (part 1)
Homework 3
Due Monday, September 23, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 2.3(a) (note: just part (a)!)
    Hint: What does \(x^*Ax\) equal? What about \((x^*Ax)^*\)?
  • T-B: 3.2
Suggested Extra Problems (not collected):
7 Wed, Sept 18 Finish Lecture 4 No assigned homework. Suggested work (not collected):
8 Mon, Sept 23 Lecture 5: More on the SVD Homework 4
Due Monday, September 30, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 4.1, 4.3
    Note: For 4.1, do not use a computer / calculator, and do not try to perform the calculations from the proof of Theorem 4.1. Instead, just think about the idea that the matrix \(A\) turns circles into ellipses, and that when we write \(A = U \Sigma V^*\), that means the circle -> ellipse transformation involves first a rotation/reflection (\(V^*\)), then a stretching along the axes (\(\Sigma\)), and finally a rotation/reflection back into place (\(U\)).

    For 4.3, refer to the posted Matlab tutorials, and feel free to search online for other tutorials about how to plot points, lines, and vectors. You should use the "svd" function in Matlab to compute the SVD. You must submit your code to me as an "mlx" file (Matlab Live) and the corresponding "pdf" version on D2L.
Suggested Extra Problems (not collected):
  • practice more Matlab!
9 Wed, Sept 25 Computing the SVD by hand
Lecture 6: Projectors
Homework 5
Due Wednesday, October 2, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 5.3(a)-(d)
10 Mon, Sept 30 Finish Lecture 6 No required homework.

Suggested Extra Problem (not collected):
  • T-B: 6.1
11 Wed, Oct 2 Lecture 7: QR Factorization Homework 6
Due Wednesday, October 9, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 6.4
  • T-B: 7.1
12 Mon, Oct 7 Finish Lecture 7
Lecture 8: Gram-Schmidt Orthogonalization
Homework 7
Due Monday, October 14, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 8.2 — Implement the Modified Gram-Schmdit Orthogonalization algorithm (Algorithm 8.1) in Matlab. Use the command "format long;" to see 16 decimal places. Run your algorithm on the matrix \(\left[\begin{array}{cc}1&2\\3&4\end{array}\right]\). Then run Matlab's internal QR Factorization algorithm with the command "[Q, R] = qr(A)". Compare the two results.
Suggested Extra Problem (not collected):
  • T-B: Read Lecture 9 about Matlab, and attempt experiments 1 and 3.
13 Wed, Oct 9 Lecture 11: Least Squares Problems No homework today.
14 Mon, Oct 14 Finish Lecture 11
Lecture 12: Conditioning and Condition Numbers
Homework 8
Due Tuesday, October 22, by 5:00pm
(Extension due to Midterm Break)
Must be submitted electronically on D2L
  • T-B: 11.3 (skip (c)). Note that "\" in Matlab solves systems of the form \(Ax=b\). Use it for Steps 3 and 4 in Algorithm 11.1. You may also use the function "chol" to compute the Cholesky factorization.
15 Wed, Oct 16 More Lecture 12 No homework today — study for midterm.
16 Mon, Oct 21 Finish Lecture 12
Exam Review
No homework today — study for midterm.
17 Wed, Oct 23 Midterm Exam
Take-Home Exam Assigned
   due Thursday, October 31, midnight
18 Mon, Oct 28 Lecture 13: Floating Point Arithmetic
Lecture 14: Stability
No homework today — continue work on midterm.
19 Wed, Oct 30 Lecture 15: More on Stability Homework 9
Due Wednesday, November 6, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 15.1 (a),(b),(c),(d), and 15.2 (not looking for calculations, just explanations [mostly words])
Thurs, Oct 31 Take-Home Exam Due
20 Mon, Nov 4 Brief summary of:
    Lecture 17: Stability of Back Substitution
    Lecture 18: Condiioning of Least Squares
    Lecture 19: Stability of Least Squares
No homework today
21 Wed, Nov 6 Lecture 24: Eigenvalue Problems No homework today
22 Mon, Nov 11 Finish Lecture 24
Lecture 25: Overview of Eigenvalue Algorithms
No homework today
23 Wed, Nov 13 Finish Lecture 25
Lecture 26: Reduction to Hessenberg or Tridiagonal Form
Homework 10
Due Wednesday, November 20, by 2:00pm
Must be submitted electronically on D2L
  • T-B: 24.1 (a)-(e)
24 Mon, Nov 18 Lecture 27: Rayleigh Quotient, Inverse Iteration No homework today
25 Wed, Nov 20 Lecture 28: QR Algorithm Without Shifts No homework today
26 Mon, Nov 25 Finish Lecture 28
Lecture 32: Overview of Iterative Methods
No homework today
Wed, Nov 27 Thanksgiving Break — no class
27 Mon, Dec 2 Lecture 33: The Arnoldi Iteration No homework today
28 Wed, Dec 4 Lecture 34: How Arnoldi Locates Eigenvectors No homework today