BASIS
FOUNDATION MATH FOR AI
Foundation Math for AI

Learn linear algebra visually.
Practice every concept.
Track your progress.

Watch the free video lessons, then come here to actually practice — interactive widgets, guided problems, and solutions for every idea. This is the practice companion to the Basis YouTube channel.

Start practicing →▶  Watch the free videos
3
Books
10
Chapters
38
Interactive lessons
Free guide

Linear Algebra for AI — The 12 Ideas That Matter

A 15-page visual summary of everything the video course covers. Read it in fifteen minutes and the whole subject has a shape.

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Every lesson stays free — forever.

Basis is funded by the people who learn from it. If these lessons helped you, you can support the channel for the price of a coffee a month — and get early access to new chapters, the Manim source code, and your name in the credits.

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Interactive practice

Every concept has a hands-on widget and a companion video. Drag, slide, and explore — then check yourself. First lessons free

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Linear Algebra

Vectors, matrices, transformations, eigenvalues & the math behind AI.

Vectors✎ Practice7▶
01
What is a Vector? — Start Here
▶ Video
02
What is a vector
Open▶ Video
03
Operations
Open▶ Video
04
Components
Open▶ Video
05
Dot product
Open▶ Video
06
Magnitude
Open▶ Video
07
Unit vector
Open▶ Video
Matrices6▶
01
Matrix anatomy
Open▶ Video
02
Add scalar
Open▶ Video
03
Multiplication
Open▶ Video
04
Identity
Open▶ Video
05
Transpose
Open▶ Video
06
Special
Open▶ Video
Linear Transformations3▶
01
Matrix as function
Open▶ Video
02
Four transforms
Open▶ Video
03
Composition
Open▶ Video
Systems of Equations3▶
01
Ax equals b
Open▶ Video
02
Gaussian elimination
Open▶ Video
03
Solution types
Open▶ Video
Determinants3▶
01
Determinant meaning
Open▶ Video
02
Computing
Open▶ Video
03
Singular
Open▶ Video
Matrix Inverse3▶
01
What is inverse
Open▶ Video
02
Solving systems
Open▶ Video
03
Inverse and determinant
Open▶ Video
Vector Spaces & Subspaces4▶
01
Span
Open▶ Video
02
Independence
Open▶ Video
03
Basis dimension
Open▶ Video
04
Rank
Open▶ Video
Eigenvalues & Eigenvectors3▶
01
Eigen geometry
Open▶ Video
02
Computing eigen
Open▶ Video
03
Why it matters
Open▶ Video
Special Decompositions3▶
01
Eigendecomposition
Open▶ Video
02
SVD
Open▶ Video
03
SVD in ML
Open▶ Video
AI Applications3▶
01
Data as vectors
Open▶ Video
02
PCA
Open▶ Video
03
Neural network layer
Open▶ Video

Calculus (High School)

Limits, derivatives, integrals and their applications — visual and intuitive.

⏳ Coming soon

Calculus (High School) is in production

The full Calculus (High School) course — visual video lessons plus interactive practice, in the same style as Linear Algebra — is being built right now. Here's what's on the way:

Unit 1 · Limits & Continuity
Unit 2 · Derivatives
Unit 3 · Applications of Derivatives
Unit 4 · Integrals
Unit 5 · Applications of Integrals
Get notified when Calculus drops →
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Statistics

Data, probability, distributions, inference & the statistics behind ML.

⏳ Coming soon

Statistics is in production

The full Statistics course — visual video lessons plus interactive practice, in the same style as Linear Algebra — is being built right now. Here's what's on the way:

Unit 1 · Descriptive Statistics
Unit 2 · Probability
Unit 3 · Random Variables & Distributions
Unit 4 · Inferential Statistics
Unit 5 · Regression & Modeling
Unit 6 · AI/ML Capstone
Get notified when Statistics drops →
One email when it goes live. No spam, unsubscribe anytime.