Domain Neighborhood
Linear Algebra
Vectors, matrices, and linear maps: the language of representations, optimization, and modern deep learning.
Recommended Route
Start here, then follow the prerequisites forward.
This sequence is ordered for learning rather than inventory: lower difficulty, fewer prerequisites, and more central concepts come first.
- 01Vector Spaces
A vector space is a set of objects you can add and scale, where those operations behave consistently.
10 mincodedemoentry pointEntry point: build the first mental model here.
- 02Dot Product
The dot product measures alignment: it connects angles, lengths, and projections, and underlies cosine similarity in ML.
12 mincodedemoafter Vector SpacesWhy this follows: Dot Product uses Vector Spaces directly.
- 03Orthogonality, Projections, and Least-Squares Geometry
Orthogonal projection turns least squares into geometry: the fitted point is closest in a subspace, and the leftover residual is perpendicular to that subspace.
18 mincodedemoafter Dot Product, Norms, Basis and SpanWhy this follows: Orthogonality, Projections, and Least-Squares Geometry uses Dot Product directly.
- 04Matrix Decompositions: Eigendecomposition, SVD, and Spectral Structure
Matrix decompositions open a linear map into directions and scales: eigendecomposition works when one space has enough eigenvectors, while SVD always gives input directions, output directions, and low-rank channels.
20 mincodedemoafter Dot Product, Norms, Basis and SpanWhy this follows: both pages keep the linear algebra thread active.
- 05Rank, Null Space, Column Space, and Conditioning
Rank says which outputs a matrix can reach, null space says which inputs disappear, and conditioning says how fragile those directions are numerically.
18 mincodedemoafter Vector Spaces, Basis and Span, Linear IndependenceWhy this follows: both pages keep the linear algebra thread active.
All Published Notebooks
Browse the territory.
Vector Spaces
A vector space is a set of objects you can add and scale, where those operations behave consistently.
Dot Product
The dot product measures alignment: it connects angles, lengths, and projections, and underlies cosine similarity in ML.
Orthogonality, Projections, and Least-Squares Geometry
Orthogonal projection turns least squares into geometry: the fitted point is closest in a subspace, and the leftover residual is perpendicular to that subspace.
Matrix Decompositions: Eigendecomposition, SVD, and Spectral Structure
Matrix decompositions open a linear map into directions and scales: eigendecomposition works when one space has enough eigenvectors, while SVD always gives input directions, output directions, and low-rank channels.
Rank, Null Space, Column Space, and Conditioning
Rank says which outputs a matrix can reach, null space says which inputs disappear, and conditioning says how fragile those directions are numerically.
In Progress