Linear Algebra
Use vectors — a way of describing a move in space — to program a game and design a logo.
Meet Vectors
Adding Vectors
From One to Another
Length of a Vector
Scaling Vectors
Between Two Vectors
Moving Along a Line
Transformations with Vectors
Translations
Dilations
Reflections
Length and Direction
Polar Coordinates
Polar to Rectangular
Cosine and Sine
Vectors in Any Direction
Rotations
Speed Boosts
The Dot Product
A Formula for Dot Product
Dot Product and Direction
Dot Product with Components
What is a Vector?
Waves as Abstract Vectors
Why Vector Spaces?
The Gauss-Jordan Process I
The Gauss-Jordan Process II
Application: Markov Chains I
Real Euclidean Space I
Real Euclidean Space II
Span & Subspaces
Coordinates & Bases
Matrix Subspaces
Application: Coding Theory
Application: Graph Theory I
What Is a Matrix?
Linear Transformations
Matrix Products
Matrix Inverses
Application: Image Compression I
Application: Cryptography
Bivectors
Trivectors & Determinants
Determinant Properties
Multivector Geometry
Dual Space
Tensors & Forms
Tensor Products
Wedges & Determinants
Application: Markov Chains II
Eigenvalues & Eigenvectors
Diagonalizability
Normal Matrices
Jordan Normal Form
Application: Graph Theory II
Application: Discrete Cat Map
Application: Arnold's Cat Map
Inner Product Spaces
Gram-Schmidt Process
Least Squares Regression
Singular Values & Vectors
Singular Value Decompositions
SVD Applications
Course description
Use vectors — a way of describing a move in space — to program a game and design a logo.
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Group Theory
Explore groups through symmetries, applications, and problems.
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