intermediateFree

Computational Linear Algebra

Name: Computational Linear Algebra
Rating: 4.6 (850 reviews)

by Rachel Thomas · fast.ai

4.6

(850 reviews)

50K+ enrolled8 weeksUpdated 2023-06

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Our Verdict

Worth it — with caveats

fast.ai's Computational Linear Algebra for Coders, created by Rachel Thomas, is a genuinely strong but narrowly-scoped free course that teaches numerical/computational linear algebra (matrix decompositions, SVD, NMF, PCA, QR, eigen-decomposition) through real applications rather than abstract theory. It pairs a free Jupyter-notebook textbook on GitHub with a YouTube lecture playlist, and was originally taught in 2017 in the University of San Francisco's MS in Analytics program after students completed a 'Linear Algebra Bootcamp'. Independent reviewers (Machine Learning Mastery, KDnuggets) praise its rare focus on the practical concerns of matrix computation, memory use, speed, and numerical stability, and its modern toolset (PyTorch, Numba, randomized SVD). The critical caveat, stated by both fast.ai and outside reviewers, is that this is NOT an introduction to linear algebra: it assumes reasonable fluency with the basics, so beginners will be left behind. It is best understood as a 'second course' for coders who already know basic linear algebra and want to implement and accelerate matrix methods.

Excellent, free, application-first material from a credible source (fast.ai / Rachel Thomas), but it explicitly assumes prior linear-algebra fluency, hasn't been substantively updated since 2017, offers no certificate, and is more self-driven (notebooks + YouTube) than a guided platform course. Take it if you already know basic linear algebra and code in Python; skip or do prep first otherwise.

Best for: Coders, data scientists, and ML practitioners who already have basic linear algebra fluency and want to understand, implement, and speed up the matrix methods (SVD, PCA, NMF, QR, eigen-decomposition) underlying real applications like topic modeling, background removal from video, CT-scan reconstruction, and PageRank. Ideal for self-directed learners comfortable working in Jupyter/Python who care about numerical stability, memory, and performance, not just calling library functions.

Skip if: Complete beginners to linear algebra (the course states it assumes fluency with the basics and recommends 3Blue1Brown's Essence of Linear Algebra as prep), learners who want a structured, certificate-bearing, hand-held platform experience, and anyone whose sole goal is applied deep learning, who would be better served by fast.ai's own Practical Deep Learning for Coders. Those wanting recently-updated 2024+ tooling should note the material dates to 2017.

About This Course

Covers matrix factorizations, SVD, PCA, and numerical linear algebra with applications to NLP and image processing.

What You'll Learn

Topic modeling on text using Non-negative Matrix Factorization (NMF) and Singular Value Decomposition (SVD), with TF-IDF

Separating foreground/background in video via Robust PCA (matrix decomposition)

Compressed sensing and CT-scan image reconstruction using robust regression

Implementing linear regression multiple ways and predicting health outcomes

Google's PageRank via eigenvalue/eigen decomposition and the power method

Implementing QR factorization (Gram-Schmidt and Householder transformations) and LU factorization

The numerical-computing concerns that libraries hide: floating-point precision, machine epsilon, numerical stability, memory use, speed, vectorization, and parallelization, using NumPy, Numba, and PyTorch (including randomized SVD)

Curriculum

0. Course Logistics

Orientation plus linear algebra review resources for getting up to speed.

1. Why are we here?

Motivation and the central question: doing matrix computations with acceptable speed and accuracy; matrix/tensor products as a foundation.

2. Topic Modeling with NMF and SVD

Decompose a document-term matrix to find topics using SVD and NMF, with TF-IDF and SGD.

3. Background Removal with Robust PCA

Use Robust PCA to separate static background from moving foreground in surveillance video.

4. Compressed Sensing with Robust Regression

Reconstruct CT-scan images from limited measurements using robust regression and compressed sensing.

5. Predicting Health Outcomes with Linear Regressions

Apply linear regression to a real prediction problem.

6. How to Implement Linear Regression

Implement linear regression from the ground up, comparing approaches and discussing regularization.

7. PageRank with Eigen Decompositions

Compute Google's PageRank using eigenvalue decomposition and the power method.

8. Implementing QR Factorization

Build QR factorization via Gram-Schmidt and Householder transformations.

Prerequisites

Working knowledge of basic linear algebra (vectors, matrices, matrix multiplication, notation) - the course assumes 'reasonable fluency with the basics' and is explicitly not an intro
Comfort programming in Python and using Jupyter notebooks
Familiarity with NumPy; exposure to scikit-learn helpful
Recommended prep for those rusty on the math: 3Blue1Brown 'Essence of Linear Algebra' video series

Instructor

Rachel Thomas

Instructor · fast.ai

Pros & Cons

Pros

Completely free with no ads: full Jupyter-notebook textbook on GitHub plus a YouTube lecture playlist, from a highly credible source (fast.ai co-founder Rachel Thomas, USF)
Rare application-first ('top-down') approach: every concept is anchored to a real problem (CT scans, video background removal, PageRank, topic modeling), which independent reviewers say keeps motivation high
Strong emphasis on the practical engineering concerns most math courses ignore: numerical stability/precision, memory, speed, and how to accelerate algorithms
Modern, hands-on tooling for its time: PyTorch, Numba (Python-to-C), scikit-learn, NumPy, and randomized SVD, so you implement methods rather than only invoking them
Independently well-reviewed (Machine Learning Mastery calls it 'excellent'; KDnuggets highlights the modern algorithms and debugging/acceleration value)

Cons

Not for beginners: explicitly assumes prior linear-algebra fluency, so newcomers will be left behind without doing prep first
Dated material (taught summer 2017, repository not substantively updated since); tooling and library APIs have moved on, even if the math is timeless
Self-directed format (notebooks + unlisted-style YouTube videos + forums) with no graded path, no instructor support today, and no certificate of completion
Narrow scope: it is numerical linear algebra, not a general ML or deep-learning course; overkill if your only goal is applied deep learning

Alternatives To Consider

Mathematics for Machine Learning and Data Science Specialization

Coursera

View course

Practical Deep Learning for Coders

fast.ai

View course

Machine Learning

Stanford Online

View course

Frequently Asked Questions

Is Computational Linear Algebra free?

Yes — Computational Linear Algebra is free to access. Free. The notebook textbook is open-source on GitHub (fastai/numerical-linear-algebra) and the lectures are free on YouTube; no payment, no paywall, and no certificate is offered.

Who is Computational Linear Algebra for?

Coders, data scientists, and ML practitioners who already have basic linear algebra fluency and want to understand, implement, and speed up the matrix methods (SVD, PCA, NMF, QR, eigen-decomposition) underlying real applications like topic modeling, background removal from video, CT-scan reconstruction, and PageRank. Ideal for self-directed learners comfortable working in Jupyter/Python who care about numerical stability, memory, and performance, not just calling library functions.

What will you learn in Computational Linear Algebra?

Topic modeling on text using Non-negative Matrix Factorization (NMF) and Singular Value Decomposition (SVD), with TF-IDF; Separating foreground/background in video via Robust PCA (matrix decomposition); Compressed sensing and CT-scan image reconstruction using robust regression; Implementing linear regression multiple ways and predicting health outcomes.

What are the prerequisites for Computational Linear Algebra?

Working knowledge of basic linear algebra (vectors, matrices, matrix multiplication, notation) - the course assumes 'reasonable fluency with the basics' and is explicitly not an intro; Comfort programming in Python and using Jupyter notebooks; Familiarity with NumPy; exposure to scikit-learn helpful; Recommended prep for those rusty on the math: 3Blue1Brown 'Essence of Linear Algebra' video series.

Is Computational Linear Algebra worth it?

How we reviewed this course

This is an independent editorial assessment by Cursarium, based on fast.ai's published course materials and aggregated public learner feedback (last reviewed 2026-06). We have not independently completed the course. Links to providers are standard references, not paid placements.

Sources

Free

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