Neural networks are matrix multiplications. Embeddings are vectors. PCA is eigendecomposition. This course teaches the linear algebra that machine learning runs on — with Python and NumPy so the math is tangible, not abstract.
This is a text-first course that links out to the best supporting material on the internet instead of trying to replace it. The goal is to make this the best course on linear algebra and machine learning mathematics you can find — even without producing a single minute of custom video.
This course is built by people who ship production linear systems for a living. It reflects how things actually work on real projects — not how the documentation describes them.
Every day has working code snippets you can paste into your editor and run right now. The emphasis is on understanding what each line does, not memorizing syntax.
Instead of shooting videos that go stale in six months, Precision AI Academy links to the definitive open-source implementations, official documentation, and the best conference talks on the topic.
Each day is designed to finish in about an hour of focused reading plus hands-on work. You can do the whole course over a week of lunch breaks. No calendar commitment, no live classes, no quizzes.
Each day stands alone. Read them in order for the full picture, or jump straight to the day that answers the question you have today.
Vectors as arrows in space, dot products as similarity measures, cross products, and vector norms. How cosine similarity works and why it’s used for embedding search.
Matrix multiplication, transpose, identity, inverse, and how matrix operations correspond to geometric transformations. NumPy implementations for all operations.
Determinants as area/volume scaling factors, Gaussian elimination for solving linear systems, and LU decomposition. Why singular matrices cause problems in ML.
What eigenvalues and eigenvectors represent geometrically. Power iteration, the characteristic polynomial, and diagonalization. The foundation for PCA and spectral methods.
Principal Component Analysis derived from scratch, SVD, how neural network weight matrices are initialized, and the linear algebra inside attention mechanisms.
Instead of shooting our own videos, Precision AI Academy links to the best deep-dives already on YouTube. Watch them alongside the course. All external, all free, all from builders who ship this stuff.
The most beautiful visual explanation of vectors, matrices, and eigenvalues. Watch this alongside every day of the course.
How linear algebra maps to ML operations: matrix multiplications in neural networks, embeddings, and PCA.
Implementing vectors, matrices, and eigendecomposition with NumPy. The computational side of every mathematical concept in this course.
Principal Component Analysis from the linear algebra up — covariance matrices, eigenvectors, and dimensionality reduction.
The best way to understand any technology is to read the production-grade implementations that prove it works. These repositories implement patterns from every day of this course.
The computational backbone of this course. The linalg module implements every operation in Days 2-5 with optimized BLAS/LAPACK.
Scientific computing library with sparse matrix support, advanced eigenvalue solvers, and signal processing linear algebra.
The ML framework where linear algebra becomes neural networks. The torch.linalg module and autograd source show how differentiation of matrix ops works.
Practical Deep Learning for Coders. The chapters on matrix multiplication and embedding explain exactly how this course’s math becomes working ML models.
You run models but don’t fully understand why attention mechanisms work or how PCA chooses components. This course answers both.
Every ML course assumes linear algebra. This course teaches the specific subset that machine learning actually uses — not the full undergraduate curriculum.
Transformer papers are 80% linear algebra notation. This course gives you the background to read them without a math PhD.
The 2-day in-person Precision AI Academy bootcamp covers linear algebra and machine learning mathematics hands-on. 5 U.S. cities. $1,490. 40 seats max. June–October 2026 (Thu–Fri).
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