Linear Algebra @BUCS
UNDER CONSTRUCTION

This is a (very early draft) set of notes for CAS CS 132: Geometric Algorithms at Boston University. Admittedly, I was unsure if I wanted to take on this project (in a sense, I still am). I'm not convinced there's a need for another collection of notes on linear algebra. But it turns out I can't help myself. I am of the opinion that any good course needs to be personal, so these are my personal notes, which follow my way of thinking about and organizing the material. It's also my excuse to play around with building visualizations (all of which are pretty much hand-spun using Elm).

These notes are based heavily on Linear Algebra, Geometry, and Computation by Mark Crovella, which are in turn based heavily on Linear Algebra and Its Applications by David C. Lay, Judy J. McDonald, and Steven R. Lay (a mainstay in undergraduate texts on linear algebra).

Solving Linear Systems

Vectors

  • Vector Equations
  • Matrix-Vector Equations
  • Linear Independence

Linearity

  • Linear Transformations
  • Matrices of Linear Transformations

More on Matrices

  • Matrix Algebra
  • Matrix Inverses
  • Invertible Matrix Theorem

Applications

  • Algebraic Graph Theory
  • Markov Chains
  • LU Decomposition

Vector Spaces

  • Subspaces
  • Dimension and Rank

Eigenvalues

  • Eigenvalues and Eigenvectors
  • The Characteristic Equation
  • Diagonalization

Analytic Geometry

  • Orthogonality
  • Least Squares