Geometry → Representation → ML
From coordinates and projections to semantic spaces and statistical manifolds.
- 1Part 1
Basis: Choosing Coordinates for a World
A basis is not the vector space; it is the coordinate language we choose to describe it.
- 2Part 2
Projection: The Shadow of a Vector
Orthogonal projection turns the intuitive idea of a shadow into one of linear algebra's most useful operations.
- 3Part 3
Cosine Similarity: When Angle Becomes Meaning
Normalize the dot product and vector angle becomes a practical measure of similarity.
- 4Part 4
Linear Transformations: Functions That Respect Geometry
See matrices as machines that transform entire grids rather than as rectangular tables of numbers.
- 5Part 5
Eigenvectors: Directions That Refuse to Turn
Some directions survive a linear transformation without changing direction. Those are eigenvectors.
- 6Part 6
Covariance: How Variables Move Together
From scatter clouds to covariance ellipses, principal directions and positive semidefinite matrices.
- 7Part 7
Word2Vec: When Words Acquire Geometry
How prediction turns words into points, neighborhoods and surprisingly useful directions.
- 8Part 8
Information Geometry: When Probability Distributions Become Points
A first walk through statistical manifolds, Fisher information and the geometry hidden inside probability.