[ToDo] Linear Algebra

Dated Apr 26, 2020; last modified on Mon, 05 Sep 2022

Linear Systems

  • Solving Linear Systems
  • Linear Geometry
  • Reduced Echelon Form
  • Topic: Computer Algebra Systems
  • Topic: Input-Output Analysis
  • Topic: Accuracy of Computations
  • Topic: Analyzing Networks

Vector Spaces

  • Definition of Vector Space
  • Linear Independence
  • Basis and Dimension
  • Topic: Fields
  • Topic: Crystals
  • Topic: Voting Paradoxes
  • Topic: Dimensional Analysis

Maps Between Spaces

  • Isomorphisms
  • Homomorphisms
  • Computing Linear Maps
  • Matrix Operations
  • Change of Basis
  • Projection
  • Topic: Line of Best Fit
  • Topic: Geometry of Linear Maps
  • Topic: Magic Squares
  • Topic: Markov Chains
  • Topic: Orthonormal Matrices

Determinants

  • Definition
  • Geometry of Determinants
  • Laplace’s Formula
  • Topic: Cramer’s Rule
  • Topic: Speed of Calculating Determinants
  • Topic: Chiò’s Method
  • Topic: Projective Geometry
  • Topic: Computer Graphics

Similarity

  • Complex Vector Spaces
  • Similarity
  • Nilpotence
  • Jordan Form
  • Topic: Method of Powers
  • Topic: Stable Populations
  • Topic: Page Ranking
  • Topic: Linear Recurrences
  • Topic: Coupled Oscillators

Appendix

  • Statements
  • Quantifiers
  • Techniques of Proof
  • Sets, Functions, and Relations
Linear Algebra. Jim Hefferon. joshua.smcvt.edu . 2020.