Linear Algebra Videos
and Guided Notes
Welcome to our Linear Algebra Videos and Guided Notes page! This resource is designed to help you learn fundamental linear algebra concepts. Whether you're learning linear algebra for the first time or just need to review some concepts, our materials are here to support you.
What You'll Find Here
Video Lessons
Our linear algebra videos cover all the essential topics and concepts in a clear and comprehensive manner. Each video is structured to provide straightforward explanations, practical examples, and step-by-step solutions. These videos are perfect for understanding key concepts.
Interactive Guided Notes
To complement our videos, we offer downloadable guided notes. These notes are designed to be filled in as you watch the videos, ensuring active engagement with the material. Guided notes help you to:
Reinforce Understanding: By filling in key information as you review, you solidify your grasp of linear algebra concepts.
Enhance Retention: Active note-taking aids in embedding the information in your memory.
Organize Your Study Materials: Keep your notes well-organized and easily accessible for future review and exam preparation.
How to Use These Resources
Watch the Videos: Begin by watching our linear algebra review videos. Each lesson is designed to build on your existing knowledge and clarify complex topics.
Download the Guided Notes: Access the guided notes provided with each video. These are available in PDF format for easy download and printing.
Follow Along and Fill In: As you watch the videos, fill in the guided notes. This process will help you engage with the material and retain the information more effectively.
Review and Study: Use your completed notes as a valuable study aid for reviewing key concepts and preparing for exams.
Start Learning Today!
Click on the links below to access the linear algebra videos and guided notes. New videos and notes will be added each week starting the last week of August 2024, and the series will be complete by the second week of December 2024. The course outline primarily follows the order of topics found in the textbook Linear Algebra and Applications by David Lay, Steven Lay, and Judi McDonald.
Course Outline
0. Introduction
1. Linear Equations in Linear Algebra
1.1 Systems of Linear Equations - Introduction
1.1 Systems of Linear Equations - Part 1
1.1 Systems of Linear Equations - Part 2
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations- Part 1
1.7 Linear Independence
1.3 Vector Equations - Part 2 (Span)
1.4 The Matrix Equation Ax=b
1.10 Difference Equations
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.8/1.9 Linear and Matrix Transformations Part 1
1.8/1.9 Linear and Matrix Transformations Part 2
2. Matrix Algebra
2.1 Matrix Operations Part 1
2.1 Matrix Operations Part 2
2.2 The Inverse of a Matrix Part 1
2.2 The Inverse of a Matrix Part 2
2.2 The Inverse of a Matrix Part 3
3. Determinants
3.1 Introduction to Determinants Part 1
3.1 Introduction to Determinants Part 2
3.2 Properties of Determinants
4. Vector Spaces
4.1. Vector Spaces and Subspaces
4.3. Linearly Independent Sets; Bases
4.2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations
5. Eigenvalues and Eigenvectors
5.1. Eigenvalues and Eigenvectors
5.2. The Characteristic Equation Part 1
5.2. The Characteristic Equation Part 2
5.3. Diagonalization Part 1
5.3. Diagonalization Part 2
5.3. Diagonalization Part 3
6. Orthogonality and Least Squares
6.1 Inner Product, Length, and Orthogonality
6.2. Orthogonal Sets
6.3. Orthogonal Projections
6.4. The Gram-Schmidt Process
6.5. Least-Squares Problems Part 1
6.5. Least-Squares Problems Part 2
Additional Topics
7.4 The Singular Value Decomposition
9.4 Duality