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Linear Algebra 101

From vectors to eigenvalues — build real linear algebra intuition through interactive geometric visualizations and matrix operations.

12 Modules 12 hands-on labs Beginner
Linear Algebra Vectors Matrices Eigenvalues Transformations
Start Module 1 → View All Modules
Outcomes

What You'll Learn

Vector Operations
Master dot products, cross products, and vector spaces with geometric intuition.
Matrix Algebra
Perform matrix multiplication, inversion, and decomposition confidently.
Linear Transformations
Visualize and understand rotations, reflections, and projections.
Eigenanalysis
Compute eigenvalues and eigenvectors and understand their geometric meaning.
SVD & PCA
Apply singular value decomposition and principal component analysis to real data.
Practical Applications
Use linear algebra in machine learning, computer graphics, and engineering.
Curriculum

Course Modules

12 modules from vectors and matrices to real-world linear algebra applications.

1
Vectors & Spaces
4 lessons1 lab
Start Here
What is Linear Algebra?Slides
Scalars, Vectors & MatricesSlides
Geometric InterpretationSlides
Vector Spaces and SubspacesSlides
2
Matrices & Linear Transformations
4 lessons1 lab
Available
What is a Matrix?Slides
Matrix OperationsSlides
Linear TransformationsSlides
Inverse and DeterminantSlides
3
Systems of Linear Equations
4 lessons1 lab
Available
Setting Up Linear SystemsSlides
Gaussian EliminationSlides
Solution TypesSlides
Applications of Linear SystemsSlides
4
Eigenvalues & Eigenvectors
4 lessons1 lab
Available
The Eigenvalue ProblemSlides
Finding EigenvectorsSlides
DiagonalizationSlides
Applications of EigenvaluesSlides
5
Orthogonality
4 lessons1 lab
Available
Orthogonal Vectors and ProjectionsSlides
The Gram-Schmidt ProcessSlides
Orthogonal MatricesSlides
Least SquaresSlides
6
Inner Product Spaces
3 lessons1 lab
Available
Inner ProductsSlides
Function SpacesSlides
Fourier Series ConnectionSlides
7
Matrix Decompositions
4 lessons1 lab
Available
LU DecompositionSlides
QR DecompositionSlides
Singular Value DecompositionSlides
Cholesky DecompositionSlides
8
Vector Calculus Connections
3 lessons1 lab
Available
Gradients and JacobiansSlides
Optimization with Linear AlgebraSlides
Linear Algebra in Machine LearningSlides
9
Numerical Linear Algebra
3 lessons1 lab
Available
Floating Point and ConditioningSlides
Iterative MethodsSlides
Sparse MatricesSlides
10
Applications in Signal Processing
3 lessons1 lab
Available
Convolution as Matrix MultiplicationSlides
Filter Design with Linear AlgebraSlides
PCA and Dimensionality ReductionSlides
11
Applications in Machine Learning
3 lessons1 lab
Available
Linear ModelsSlides
Matrix FactorizationSlides
Neural Network FundamentalsSlides
12
Capstone & What's Next
3 lessons1 project
Available
Putting It All TogetherSlides
Advanced Topics PreviewSlides
Resources & Career PathsSlides
Before You Start

Prerequisites

Ready to start Linear Algebra?

Begin with Module 1 and discover the mathematical language that powers modern technology.

Start Module 1 →
Labs & Demos 8 interactive demos — 8 interactive demos