Learn matrix decompositions via CT scans and surveillance footage

What it does

This repository holds the Jupyter notebooks and video links for the University of San Francisco’s 2017 Computational Linear Algebra course. It walks through foundational matrix concepts—decompositions, accuracy, memory use, and parallelization—then applies them to concrete problems like topic modeling, surveillance video background removal, and compressing CT scans. The material is built in Python using NumPy, Scikit-Learn, Numba, and occasional PyTorch.

The interesting bit

Instead of starting with proofs, each lesson anchors abstract matrix operations to an immediate practical payoff: you learn randomized SVD because you need to separate pedestrians from a static background, and you study sparse matrices because they let you reconstruct a CT image from less radiation exposure. It is essentially a cookbook for the linear algebra that actually shows up in production pipelines.

Key highlights

• Covers SVD, NMF, LU, QR, and Cholesky factorizations through applied examples rather than derivations
• Includes a full notebook on implementing linear regression from scratch, comparing naive approaches against the methods used by Scikit-Learn
• Uses Numba to compile Python to C for performance-critical sections and introduces PyTorch for GPU acceleration in select lessons
• Accompanied by a YouTube lecture playlist where the instructor reviews previous concepts at the start of each video
• Taught as part of a formal MS in Analytics program, so the pacing assumes you have some prior exposure to linear algebra

Caveats

• The course dates to 2017, so expect library references and tooling from that era
• The README is essentially a long table of contents; the actual explanations live inside the notebooks or lecture videos

Verdict

Worth bookmarking if you are a data scientist or ML engineer who knows some linear algebra but wants to see how decompositions map to real implementation trade-offs. Skip it if you are looking for a pure math reference or a quick API cheat sheet.