Free Course
Linear Algebra (Full Course)
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Course curriculum
1 sections · 84 lessons · 10h total
Course Material
What's the big idea of Linear Algebra? **Course Intro**
12:58
What is a Solution to a Linear System? **Intro**
5:28
Visualizing Solutions to Linear Systems - - 2D & 3D Cases Geometrically
8:19
Rewriting a Linear System using Matrix Notation
3:10
Using Elementary Row Operations to Solve Systems of Linear Equations
7:27
Using Elementary Row Operations to simplify a linear system
9:35
Examples with 0, 1, and infinitely many solutions to linear systems
6:30
Row Echelon Form and Reduced Row Echelon Form
6:41
Back Substitution with infinitely many solutions
11:05
The Gaussian Algorithm Visualized
13:37
What is a vector? Visualizing Vector Addition & Scalar Multiplication
6:40
Introducing Linear Combinations & Span
9:34
How to determine if one vector is in the span of other vectors?
5:00
Matrix-Vector Multiplication and the equation Ax=b
6:59
Matrix-Vector Multiplication Example
4:33
Proving Algebraic Rules in Linear Algebra --- Ex: A(b+c) = Ab +Ac
8:25
The Big Theorem, Part I
14:01
Writing solutions to Ax=b in vector form
4:48
Geometric View on Solutions to Ax=b and Ax=0.
6:21
Three nice properties of homogeneous systems of linear equations
7:53
Linear Dependence and Independence - Geometrically
8:16
Determining Linear Independence vs Linear Dependence
6:39
Making a Math Concept Map | Ex: Linear Independence
7:10
Transformations and Matrix Transformations
5:16
Three examples of Matrix Transformations
8:25
Linear Transformations
8:28
Are Matrix Transformations and Linear Transformation the same? Part I
3:04
Every vector is a linear combination of the same n simple vectors!
6:37
Matrix Transformations are the same thing as Linear Transformations
8:49
Finding the Matrix of a Linear Transformation
9:18
One-to-one, Onto, and the Big Theorem Part II
9:30
The motivation and definition of Matrix Multiplication
10:12
Computing matrix multiplication
5:37
Visualizing Composition of Linear Transformations **aka Matrix Multiplication**
14:00
Elementary Matrices
7:20
You can "invert" matrices to solve equations...sometimes!
7:12
Finding inverses to 2x2 matrices is easy!
3:04
Find the Inverse of a Matrix
6:30
When does a matrix fail to be invertible? Also more "Big Theorem".
8:45
Visualizing Invertible Transformations (plus why we need one-to-one)
8:12
Invertible Matrices correspond with Invertible Transformations **proof**
6:38
Determinants - a "quick" computation to tell if a matrix is invertible
9:14
Determinants can be computed along any row or column - choose the easiest!
3:43
Vector Spaces | Definition & Examples
8:11
The Vector Space of Polynomials: Span, Linear Independence, and Basis
12:50
Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples
6:26
The Span is a Subspace | Proof + Visualization
5:03
The Null Space & Column Space of a Matrix | Algebraically & Geometrically
10:41
The Basis of a Subspace
3:53
Finding a Basis for the Nullspace or Column space of a matrix A
9:45
Finding a basis for Col(A) when A is not in REF form.
2:37
Coordinate Systems From Non-Standard Bases | Definitions + Visualization
6:34
Writing Vectors in a New Coordinate System **Example**
3:52
What Exactly are Grid Lines in Coordinate Systems?
5:16
The Dimension of a Subspace | Definition + First Examples
5:11
Computing Dimension of Null Space & Column Space
3:27
The Dimension Theorem | Dim(Null(A)) + Dim(Col(A)) = n | Also, Rank!
4:02
Changing Between Two Bases | Derivation + Example
7:55
Visualizing Change Of Basis Dynamically
7:42
Example: Writing a vector in a new basis
8:55
What eigenvalues and eigenvectors mean geometrically
9:09
Using determinants to compute eigenvalues & eigenvectors
4:36
Example: Computing Eigenvalues and Eigenvectors
7:33
A range of possibilities for eigenvalues and eigenvectors
9:47
Diagonal Matrices are Freaking Awesome
6:28
How the Diagonalization Process Works
7:30
Compute large powers of a matrix via diagonalization
3:01
Full Example: Diagonalizing a Matrix
10:08
COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**
14:10
Visualizing Diagonalization & Eigenbases
9:46
Similar matrices have similar properties
8:47
The Similarity Relationship Represents a Change of Basis
9:59
Dot Products and Length
7:23
Distance, Angles, Orthogonality and Pythagoras for vectors
8:14
Orthogonal bases are easy to work with!
4:50
Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Complement
3:57
The geometric view on orthogonal projections
11:07
Orthogonal Decomposition Theorem Part II
11:25
Proving that orthogonal projections are a form of minimization
7:05
Using Gram-Schmidt to orthogonalize a basis
11:21
Full example: using Gram-Schmidt
6:18
Rotation Matrices || Linear Algebra Fundamentals
21:24
Least Squares Approximations
7:28
Reducing the Least Squares Approximation to solving a system
5:36
Course description
Full course description coming soon.
What you'll learn
Professional skill mastery with structured, progressive lessons
Hands-on real-world projects to build your portfolio
Industry best practices used at top-tier companies
Expert-level techniques that set you apart from peers
Certificate of completion to showcase your achievement
Lifetime access with all future updates included
Requirements
No prior experience required. A computer with internet access and a willingness to learn is all you need.
Your instructor
DT
Dr. Trefor Bazett
Senior Practitioner & Educator
12+ years exp.
3 courses
2,064 students
A seasoned professional with years of hands-on industry experience. Their teaching philosophy centres on practical, no-nonsense instruction that bridges theory and real-world application.
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