The fastai/numerical-linear-algebra repository is a free online textbook consisting of Jupyter notebooks that accompany the fast.ai Computational Linear Algebra course. Originally taught at the University of San Francisco's Masters of Science in Analytics program during summer 2017, the course addresses the fundamental question of how to perform matrix computations with acceptable speed and accuracy. The repository serves as a comprehensive educational resource for graduate students studying to become data scientists, combining theoretical concepts with practical implementation using Python.
The course material is delivered through Jupyter Notebooks and utilizes several key libraries including Scikit-Learn and Numpy for most lessons, with Numba for compiling Python to C for improved performance and PyTorch as an alternative to Numpy for GPU computation in select lessons. The repository is complemented by a YouTube playlist of lecture videos that provide additional perspective on the course material, allowing learners to revisit concepts from different angles or at a slower pace when needed.
The curriculum covers foundational concepts in numerical linear algebra starting with course logistics and an overview of matrix and tensor products, matrix decompositions, accuracy considerations, memory usage, speed optimization, and parallelization and vectorization techniques. The course progresses through practical applications including topic modeling using Non-negative Matrix Factorization and Singular Value Decomposition on the newsgroups dataset, background removal from surveillance video using Robust PCA with randomized SVD and LU factorization, and compressed sensing applications for CT scan reconstruction using robust regression techniques. Additional topics include TF-IDF calculations, stochastic gradient descent, truncated SVD, principal component analysis, L1 norm sparsity induction, LU factorization with pivoting, block matrix multiplication, sparse matrices, and L1 and L2 regression methods.
According to GitGenius classification data, the repository spans multiple domains including numerical methods, linear algebra, algorithms, machine learning, deep learning, matrix computation, optimization, scientific computing, data science, and applied mathematics. The repository maintains connections with other projects through overlapping contributors, linking to answerdotai/nbdev, ipython/ipython, and alacritty/alacritty. Community engagement is facilitated through the fast.ai discussion forums where learners can ask questions and share resources related to computational linear algebra. The repository's issue and pull request response activity shows minimal latency, with tracked contributors including la-tuna and new-guy-gif. The primary language is Jupyter Notebook, making the content directly executable and interactive for learners.
