Learn Linear Algebra:
Free Course
with 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’s Included in This Free Linear Algebra Course?
Video Lessons
Our videos cover essential linear algebra topics with clear explanations, practical examples, and step-by-step solutions. Each lesson is designed to help you build a strong foundation and confidently approach even the most complex concepts.
Free Guided Notes for Linear Algebra
Enhance your learning with downloadable guided notes, designed to be completed as you watch our videos. These notes help you:
Reinforce Understanding: Actively engage with the material by filling in key information.
Improve Retention: Strengthen your memory through hands-on learning.
Stay Organized: Create a structured resource for review and exam preparation.
How to Learn Linear Algebra Effectively
Watch the Videos: Start with our comprehensive lessons that break down topics step by step.
Download Guided Notes: Access the PDF notes for each video to follow along as you watch.
Engage Actively: Fill in the notes while watching to reinforce your understanding and retain key concepts.
Review and Prepare: Use your completed notes as a powerful study tool for exams or future reviews.
Start Learning Linear Algebra Now!
Discover essential linear algebra topics with our videos and guided notes, crafted to provide clear explanations and practical examples. Each resource is designed to help you confidently approach even the most challenging concepts.
Start your journey today with comprehensive lessons and interactive notes that simplify learning and enhance your understanding of linear algebra!
Review Materials are available at the end of each section
0. Introduction to Linear Algebra
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 (Population Models)
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation - Standard Matrix
1.9 The Matrix of a Linear Transformation - Geometric Transformations in R^2
1.9 The Matrix of a Linear Transformation - One-to-One and Onto Transformations
Review Materials
Exam Concept Review - Linear Systems of Equations
Exam Concept Review - Linear Transformations
Exam Review Problems - Linear Systems of Equations
YouTube Video Exam Review Problems
Exam Review Problems - Linear Transformations
YouTube Video Exam Review Problems
2. Matrix Algebra
2.1 Matrix Operations
2.2 The Inverse of a Matrix Part 1 - Inverse of a 2x2 Matrix and Solving Linear Systems
2.2 The Inverse of a Matrix Part 2 - Algorithm for Finding the Inverse of a Matrix
2.2 The Inverse of a Matrix Part 3 - Inverse Properties and Matrix Expression Simplification
2.3 Characterizations of Invertible Matrices Part 1 - The Invertible Matrix Theorem
2.3 Characterizations of Invertible Matrices Part 2 - Inverse Linear Transformations
Review Materials
Exam Review Problems - Matrix Algebra
YouTube Video Exam Review Problems
3. Determinants
3.1 Introduction to Determinants
3.2 Properties of Determinants
Review Materials
Exam Review Problems - Determinants
YouTube Video Exam Review Problems
4. Vector Spaces
4.1. Vector Spaces and Subspaces
4.2 Null Space and Column Space
4.3 Linearly Independent Sets - Basis
4.3 Linearly Independent Sets - Basis of Null Space and Column Space
4.5 Dimension of a Vector Space
Review Materials
Exam Review Problems - Vector Spaces
YouTube Video Exam Review Problems
5. Eigenvalues and Eigenvectors
5.1. Eigenvalues and Eigenvectors
5.2. The Characteristic Equation
5.3. Diagonalization
5.3 Application Problem - Long Term Behavior of a Population
Review Materials
Exam Review Problems - Eigenvalues and Eigenvectors
YouTube Video Exam Review Problems
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
7.4. Singular Value Decomposition
Review Materials
Exam Review Problems - Orthogonality and Least Squares
YouTube Video Exam Review Problems
Final Exam Review
YouTube Video - How to Study for a Math Exam
Part 1 - Linear Systems of Equations YouTube Video
Part 2 - Linear Transformations YouTube Video
Part 3 - Matrix Algebra YouTube Video
Part 4 - Determinants YouTube Video
Part 5 - Vector Spaces YouTube Video
Part 6 - Eigenvalues and Eigenvectors YouTube Video
Part 7 - Orthogonality and Least Squares YouTube Video