Linear Algebra

Course Curriculum

Chapter 1: Matrix Arithmetic

Lecture 1: Introduction and Overview

Lecture 2: Matrices and Vectors

Lecture 3: Matrix Arithmetic — Addition and Subtraction

Lecture 4: Matrix Arithmetic — Multiplication

Lecture 5: Matrix Arithmetic — Counter Examples

Lecture 6: Transpose

Lecture 7: Examples of Matrix Arithmetic (with practice problems)

Lecture 8: Dot Product

Lecture 9: Application: Adjacency Matrix

Chapter 2: Systems of Linear Equations

Lecture 1: Introduction to Systems of Linear Equations

Lecture 2: Reduced Row Echelon Form (REF)

Lecture 3: Examples of Producing REF

Lecture 4: Solving Systems of Equations

Lecture 5: Examples of Solving Systems of Equations (with practice problems)

Lecture 6: Application: Finding a Cubic Equation to Fit Points

Lecture 7: Application: Cryptography

Lecture 8: Application: Network Flow

Lecture 9: Application: Finding Average Cost of Mixture

Lecture 10: Application: Social Security Benefits Crossover Point

Chapter 3: Matrix Inverse

Lecture 1: Matrix Inverse

Lecture 2: Examples of Finding the Matrix Inverse

Lecture 3: Example of Finding the Matrix Inverse, Part 2 (with practice problems)

Lecture 4: Invertible Matrix Theorem

Chapter 4: Determinants

Lecture 1: Finding the Determinant of a 2×2 or 3×3 Matrix

Lecture 2: Finding the Determinant of Larger Matrices (with practice problems)

Lecture 3: Application: Finding the Area of a Polygon

Lecture 4: Application: Collision Detection

Chapter 5: Vector Spaces

Lecture 1: Vector Spaces

Lecture 2: Vector Space Examples

Lecture 3: Subspaces

Lecture 4: Subspace Examples

Lecture 5: Linear Combinations

Lecture 6: Span of a Vector Space

Lecture 7: Nullspace

Lecture 8: Column Space (with practice problems)

Lecture 9: Linear Independence

Lecture 10: Application: Eliminating Redundancy in a Graph

Lecture 11: Basis for a Vector Space

Lecture 12: The Standard Basis

Lecture 13: Finding a Basis for Vector Spaces of Polynomials

Lecture 14: Finding a Basis for Vector Spaces of Matrices

Lecture 15: Find a Basis for Matrices that Commute (with practice problems)

Chapter 6: Linear Transformations

Lecture 1: Linear Transformations

Lecture 2: Linear Transformation Examples, part 1

Lecture 3: Linear Transformation Examples, part 2 (with practice problems)

Lecture 4: Application: Differentiation of Polynomials

Lecture 5: Matrices as Linear Transformations

Lecture 6: Geometric Transformations

Lecture 7: Application: Computer Graphics

Lecture 8: Dimension, Rank, and Nullity

Lecture 9: Isomorphisms

Lecture 10: Application: Artificial Intelligence

Lecture 11: Coordinate Systems

Lecture 12: Coordinate System Examples

Lecture 13: Change of Basis (with practice problems)

Lecture 14: Application: Data Transmission and Error-Correcting Codes

Lecture 15: Application: Perspective Rectification in Computer Vision

Chapter 7: Orthogonality

Lecture 1: Orthogonality

Lecture 2: Orthogonal and Orthonormal Sets

Lecture 3: Application: Calculating Normal Vectors for Ray Tracing

Lecture 4: Orthogonal Basis

Lecture 5: Orthogonal Basis, Part 2

Lecture 6: Orthogonal Matrix

Lecture 7: Orthogonal Projections

Lecture 8: Orthogonal Projections, Part 2

Lecture 9: Orthogonal Projection onto a Subspace

Lecture 10: Gram-Schmidt Orthogonalization

Lecture 11: Gram-Schmidt Orthogonalization Examples (with practice problems)

Lecture 12: QR Factorization

Chapter 8: Least Squares

Lecture 1: Introduction to Least Squares

Lecture 2: Producing the Normal Equations

Lecture 3: Least Squares Examples

Lecture 4: Least Squares Examples, Part 2

Lecture 5: Linear Regression (with practice problems)

Lecture 6: Application: Fitting Models

Lecture 7: Application: Fitting a Circle to Data Points

Lecture 8: Application: Fitting Periodic Data

Chapter 9: Eigenvalues and Eigenvectors

Lecture 1: Eigenvalues and Eigenvectors

Lecture 2: Eigenvalues and Eigenvectors Examples

Lecture 3: Eigenvalues and Eigenvectors: Special Cases

Lecture 4: Trace of a Square Matrix (with practice problems)

Lecture 5: Application: Principal Component Analysis

Lecture 6: Application: Markov Chain

Chapter 10: Singular Value Decomposition

Lecture 1: Singular Value Decomposition (SVD)

Lecture 2: SVD Examples

Lecture 3: SVD Examples, Part 2 (with practice problems)

Lecture 4: General Applications of the SVD

Lecture 5: Application: Image Classification

Lecture 6: Application: Image Compression

Chapter 11: Numerical Linear Algebra