CHAPTER 02 / 40
Linear Algebra
8 lessons · Explore, experiment and understand.
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Vectors, matrices and linear maps are how every model — from logistic regression to transformers — stores parameters and moves data forward.
- MLPs
- embeddings
- linear layers
- Step 2~20m35⚡Challenge
Systems of Linear Equations
A system of linear equations is a collection of equations in which each unknown appears only to the first power and is never multiplied by a…
Open lesson - Step 3~20m3D · 135★Most cinematic⚡Challenge
Matrices
A matrix is a rectangular array of numbers arranged into rows and columns. We denote an matrix as , where is the number of rows and is the n…
Open lesson - Step 4~15m15⚡Challenge
Solving Systems of Linear Equations
Now that we have matrices, we can formalize how to solve . The canonical algorithm is Gaussian elimination. The idea: apply a sequence of el…
Open lesson - Step 5~20m3D · 115⚡Challenge
Vector Spaces
So far we have worked with concrete vectors in . The true power of linear algebra, however, comes from abstracting: a vector space over the…
Open lesson - Step 6~20m25⚡Challenge
Linear Independence
A set of vectors is linearly independent if the only way to form the zero vector as is with all . If any non-trivial combination gives zero,…
Open lesson - Step 7~20m3D · 125★Most cinematic⚡Challenge
Basis and Rank
A basis of a vector space is a set of vectors that is both linearly independent and spanning — every vector in can be written as a unique li…
Open lesson - Step 8~20m3D · 125★Most cinematic⚡Challenge
Linear Mappings
A linear mapping (or linear transformation) between vector spaces and is a function that respects both vector operations: for all and scalar…
Open lesson - Step 9~20m25⚡Challenge
Affine Spaces
An affine space is, roughly, a vector space that has forgotten where its origin is. Formally, an affine subspace of a vector space is a set…
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