ECE 586: Vector Space Methods with Applications (FA26)

Course Information

• Syllabus (updated 08/09/26)

  • Lecture: Gross Hall 324 MW 10:05 - 11:20 AM

  • Discussion: Gross Hall 324 F 10:05 - 11:20 AM

  • TA: TBD

  • Dr. Pfister Office Hour: Gross Hall 305 TH 3:30-4:30

Primary Sources

• Lecture Notes

  • Course Introduction

  • Chapter 1 Notes

  • Chapter 2 Notes

  • Chapter 3 Notes

  • Additional to be added, one per chapter
    

• Textbook

  • Contents (including date of last update)

  • Chapter 1: Logic and Set Theory

  • Chapter 2: Metric Spaces and Topology

  • Chapter 3: Linear Algebra

  • Chapter 4: Representation and Approximation

  • Chapter 5: Optimization

  • Chapter 6: Linear Transformations and Operators

  • Chapter 7: Matrix Factorizations and Analysis

  • Chapter 8: Canonical Forms

  • Chapter 9: Singular Value Decomposition

  • Appendix and Index

  • All Chapters

• Flip Videos and Slides

  • Watch Intro, Slides Introduction, and FAQ0
    

  • Watch Video 1, Slides Video 1, and FAQ1
    

  • Watch Video 2, Slides Video 2, and FAQ2
    

  • Watch Video 3, Slides Video 3, and FAQ3
    

  • Watch Video 4, Slides Video 4, and FAQ4
    

  • Watch Video 5, Slides Video 5, and FAQ5
    

  • Watch Video 6, Slides Video 6, and FAQ6
    

  • Watch Video 7, Slides Video 7, and FAQ7
    

  • Watch Video 8, Slides Video 8, and FAQ8
    

  • Watch Video 9, Slides Video 9, and FAQ9
    

  • Watch Video 10, Slides Video 10, and FAQ10
    

  • Watch Video 11, Slides Video 11, and FAQ11
    

  • Watch Video 12, Slides Video 12, and FAQ12
    

  • Additional to be added, one per lecture
    

Handouts

• Homework 1
  

• Homework 2
  

• Homework 3
  

• Homework 4
  

• Mini-project 1: Finite-State Markov Chains
  

• Homework 5
  

• Additional to be added
  

Secondary Sources

• Textbooks

  • Linear Algebra Done Right by Sheldon Axler
    

  • Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan D. Bloch (errata)

  • Mathematical Methods and Algorithms for Signal Processing by Todd K. Moon and Wynn C. Stirling (errata)

  • Metric Spaces by Shirali and Vasudeva

  • Metric Spaces by Searcoid

  • Topology by James Munkres

  • Linear Algebra by Kenneth Hoffman and Ray Kunze

  • Optimization by Vector Space Methods by David Luenberger

• Additional references

• • Additional Problems: A Problem Book in Real Analysis by Aksoy and Khamsi

  • Additional Problems: Schaum's Outline: Linear Algebra

  • Optional Reading: The Contraction Mapping Theorem by Keith Conrad

  • Source Localization

  • Dykstra's Algorithm, ADMM, and Coordinate Descent: Connections, Insights, and Extensions by Ryan Tibshirani

  • Example Project: A Tutorial on Recursive Methods in Linear Least Squares Problems

  • Discovery of the LMS Algorithm by Widrow

Wikipedia References

• First-Order Logic, Mathematical Proof, Set Theory, Equivalence Relation, Function
  

• Metric Space, Topology, Continuous Function, Complete Metric Space, Compact Space
  

• Contraction Mapping, Field, Vector Space, (Hamel) Basis, Topological Vector Space
  

• Normed Vector Space, Banach Space, Schauder Basis, Lp and lp Spaces, Inner Product Space
  

• Gram-Schmidt Process, Orthonormal Basis, Hilbert Space, Orthogonal Projection, Dual Space
  

• Fixed-Point Theorems
  

Other Web Resources

• Nice Slides on Propositional Logic

• Russell's Paradox

• Cauchy construction of real numbers

• Cauchy completion of general metric space

• Short note on Gradients and Hessians in Hilbert Space

• Biography of Stefan Banach

• Biography of David Hilbert