- Syllabus [PDF]
- Syllabus [HTML]
- Projects [PDF] [HTML]
- Problem List [HTML][PDF]
- Grades: Advanced Linear Algebra (Math 420, Spring 2014) [Projects]
- Course Research Guide @ Collins Library

**SCLA:**A Second Course in Linear Algebra [Provisional PDF]**GVL:**Matrix Computations (Fourth Edition)**TB:**Numerical Linear Algebra**FCLA:**A First Course in Linear Algebra [Online Version]**HJ:**Matrix Analysis (Second Edition) [Errata]**SW:**A Guide to Advanced Linear Algebra**HLA:**CRC Handbook of Linear Algebra (Second Edition)**DW:**Fundamentals of Matrix Computations (Third Edition)

- SageMathCloud
- UPS Sage Server (on-campus, VPN, proxy)

- MIT Beamer Tutorial [TeX Source!]
- Beamer User Guide [Documentation Directory (w/ theme examples)]
- Technically Speaking Videos
- Open Licenses Explained

**Course Introduction**(Wednesday, January 22)**MathSciNet**(Friday, January 24)- With UPS Librarian, Eli Gandour-Rood

**Vector Spaces**(Monday, January 27)- FCLA: Chapters V, VS
- GVL: Section 2.1
- SW: Chapter 1

**Linear Transformations**(Wednesday, January 29)- FCLA: Chapter LT
- GVL: Section 2.1
- SW: Chapter 2

**Representations**(Friday, January 31)- FCLA: Chapter R
- GVL: Section 2.1
- SW: Chapter 2
- FCLA: See Solution MR.T80

**Direct Sums**(Monday, February 3)- SCLA: Fundamentals/Direct Sums
- GVL: Subsection 2.1.5
- SW: Section 1.4

**Matrix Decompositions, LU Decomposition**(Wednesday, February 5)- FCLA: Section FS, Extended Echelon Form
- Handout: MAA Monthly,
Four Subspaces and Extended Echelon Form

- FCLA: Section OD, Triangular Matrices
- SCLA: Matrix Decompositions/LU (Triangular) Decomposition
- Worksheet: LU Factorization [SageMathCloud] [SageNB] [HTML] [PDF]
- GVL: Chapter 3 (all of it)
- GVL: For pivoting, Permutation Matrices, 1.2.8--12.11
- TB: Lectures 20, 21, 22
- DW: Sections 1.7-1.9 (note LDV decomposition)
- IEEE 754
- Goldberg, What Every Computer Scientist Should Know about Floating-Point Arithmetic

**LU Decomposition (Continued)**(Friday, February 7)**Numerical Linear Algebra**(Monday, February 10)- TB: Appendix,
The Definition of Numerical Analysis

- TB: Appendix,
**Householder Reflections**(Wednesday, February 12)- SCLA: Fundamentals/Householder Reflections
- GVL: Section 5.1
- TB: Lecture 10
- HJ: Section 2.1 (and facts about unitary matrices)
- DW: Section 3.2

**Householder Reflections (continued)**(Friday, February 14)**QR Decomposition**(Monday, February 17)- SCLA: Matrix Decompositions/QR Decomposition
- GVL: Section 5.2
- TB: Lectures 7, 8 and 10
- HJ: Section 2.1
- DW: Section 3.4

**QR Decomposition (continued)**(Wednesday, February 19)**Orthogonal Complements**(Friday, February 21)- SCLA: Fundamentals/Orthogonal Complements
- GVL: Subsection 2.1.5
- TB: Lecture 2 (partially)
- HJ: Section 0.6.6
- DW: Section 3.5 (early)

**Application: Least-Squares Solutions**(Monday, February 24)- SCLA: Applications/Least Squares
- GVL: Subsection 5.3
- TB: Lecture 11
- HJ: Section 7.4.3 (with SVD)
- DW: Section 3.1, 3.3

**Least Squares (continued)**(Wednesday, February 26)- QR/Sage due before class. Sage Notebook to email announced in class.

**Q & A**(Friday, February 28)- QR Sage Demo [Sage Worksheet] [PDF]
- Discussion, Problem List

**Quiz 1**(Monday, March 3)**Jordan Canonical Form**(Wednesday, March 5)- SCLA: Invariant Subspaces

**Jordan Canonical Form (Continued)**(Friday, March 7)- SCLA: Invariant Subspaces \

**Jordan Canonical Form (Continued)**(Monday, March 10)- SCLA: Generalized Eigenspaces

**Jordan Canonical Form (Continued)**(Wednesday, March 12)- SCLA: Generalized Eigenspaces

**Jordan Canonical Form (Continued)**(Friday, March 14)- Project Proposals Due, 2 PM, on paper
- SCLA: Generalized Eigenspace Decomposition

**Jordan Canonical Form (Continued)**(Monday, March 24)- SCLA: Nilpotent Linear Transformations

**Jordan Canonical Form (Continued)**(Wednesday, March 26)- SCLA: Canonical Form for Nilpotent Linear Transformations

**Jordan Canonical Form (Concluded)**(Friday, March 28)- SCLA: Jordan Canonical Form
- SW: Sections 5.6, 5.7
- Worksheet: Jordan Canonical Form [SageMathCloud] [SageNB] [HTML] [PDF]

**Singular Value Decomposition**(Monday, March 31)- SCLA: Fundamentals/Positive Semi-Definite Matrices
- SCLA: Decompositions/Singular Value Decomposition
- TB: Lectures 4, 5
- GVL: Section 2.4

**Singular Value Decomposition (continued)**(Wednesday, April 2)- Worksheet: Visualizing the SVD [Sage Notebook Worksheet]
- Application: Numerical Rank [Sage Notebook Worksheet]
- Application: Image Compression [Sage Notebook Worksheet]

**More Decompositions**(Friday, April 4)- Cholesky: TB, Lecture 23
- Schur: FCLA, Section OD

**"Lights Out!"**(Monday, April 7)- Guest Lecture, Prof. Gary Gordon, Lafayette College
- Project Drafts Due, 2 PM

**Alternative Definitions of Determinants**(Wednesday, April 9)**Quiz 2**(Friday, April 11)**Projects Begin**(Monday, April 14)**Quiz 3**(Wednesday, May 14, 4 PM)**Curve Fitting, Projectors**(On the bubble)

- Monday, April 14, Troy Cornelius,
**Fast Matrix Multiplication**[PDF] [Presentation] - Wednesday, April 16, Imanuel Chen,
**Tournament Matrices**[PDF] [Presentation] - Wednesday, April 16, Peter Bergene,
**Applied Fuzzy Linear Algebra: Input Output Analysis**[PDF] [Presentation] - Friday, April 18, Davis Shurbert,
**Multilinear Algebra for the Undergraduate Algebra Student**[PDF] [Presentation] - Friday, April 18, Tyler Ueltschi,
**Third-Order Tensor Decompositions and their Application in Quantum Chemistry**[HTML] [PDF] [Presentation] - Monday, April 21, Aidan Meacham,
**Image Compression**[PDF] [Presentation] - Monday, April 21, Cameron Braithwaite,
**General Inner Product and Fourier Series**[PDF] [Presentation] - Wednesday, April 23, Ross MacAusland,
**The Moore-Penrose Inverse and Least Squares**[PDF] [Presentation] - Wednesday, April 23, Anna Dovzhik,
**Coding Theory: Linear-Error Correcting Codes**[PDF] [Presentation] - Friday, April 25, Hunter Wills,
**Linear Algebra for Computer Vision**[PDF] [Presentation] - Friday, April 25, Stephen Gower,
**Netflix Prize and SVD**[PDF] [Presentation] - Monday, April 28, Matt Reid,
**Pivoting for LU Factorization**[PDF] [Presentation] - Monday, April 28, Andrew Doss,
**Solving Toeplitz Systems of Equations and Matrix Conditioning**[PDF] [Presentation] - Wednesday, April 30, Brian Whetter,
**Modules Over Principal Ideal Domains**[PDF] [Presentation] - Wednesday, April 30, Spencer De Chenne,
**Minimum Polynomials of Linear Transformations**[PDF] [Presentation] - Friday, May 1, Glenna Toomey,
**Rational Canonical Form**[PDF] [Presentation] - Friday, May 1, Becky Hanscam,
**Calculating Kinetic Data by Linear Least-Square Data Fitting Methods for an Elementary Chemical Reaction**[PDF] [Presentation] - Monday, May 5, Garrett Buffington,
**Polar Decomposition of a Matrix**[PDF] [Presentation] - Monday, May 5, Jack Gilbert,
**Markov Chains, Stochastic Processes, and Advanced Matrix Decomposition**[PDF] [Presentation]

These are simply suggestions. Some I know well, some I know little about. Some are excellent choices, some will be harder than others. And you *are not* limited to just these topics.

**Spencer De Chenne**: Minimal Polynomials of Linear Transformations**Brian Whetter**: Modules over Principal Ideal Domains**Cameron Braithwaite**: General Inner Products**Garrett Buffington**: Polar Decomposition of a Matrix**Glenna Toomey**: Rational Canonical Form**Imanuel Chen**: Tournament Matrices**Davis Shurbert**: Multilinear Algebra- Zig-Zag Form (see me for citation)

**Ross MacAusland**: The Pseudoinverse**Andrew Doss**: Solving Toeplitz Systems and the Importance of Conditioning**Aidan Meacham**: Linear Algebra and Digital Images**Matt Reid**: Pivoting for LU Factorization**Troy Cornelius**: Fast Matrix Multiplication**Jack Gilbert**: Markov Chains, Doubly Stochastic Matrices- QR via Rotators
- Numerical Stability of a Specific Algorithm (two students possibly)

**Becky Hanscam**: Calculating Kinetic Constants by Least Square Curve Fitting Methods**Hunter Wills**: Computer Graphics and Computer Vision**Stephen Gower**: Netflix Prize and Singular Value Decomposition**Anna Dovzhik**: Linear Error-Correcting Codes**Peter Bergene**: Leontief Input/Output Models (Economics)**Tyler Ueltschi**: Tensor Decompositions in Quantum Chemistry- Google Page Rank and the SVD
- Least Squares and GPS (North American Datum)
- Signal Processing
- Linear Algebra for Computer Graphics

Sage is open-source software for advanced mathematics. There are many ways to use it.

- Sage Math Cloud (experimental)
- UPS Sage Notebook Server (campus or VPN only)
- Worldwide Notebook Server (popular, often slow)
- Sage Cell Server (one-off computations)

Main website for Sage: Sage Website

This is: http://buzzard.ups.edu/courses/2014spring/420s2014.html

Maintained by: Rob Beezer

Last updated: March 24, 2014