Chapter 39 — Further Reading

The capstone draws on the whole book, so this list is organized by track: a couple of anchor textbook references, then the sources most useful for the specific project you chose. Page and section pointers are to standard editions; confirm against your copy.

Foundations (all tracks)

  • Gilbert Strang, Introduction to Linear Algebra (5th ed.). The book's spiritual cousin. For the capstone, revisit the chapters on the four fundamental subspaces, least squares, eigenvalues, and the SVD — Strang's "big picture" diagram is exactly the organizing skeleton these projects rest on. His MIT OpenCourseWare lectures (18.06) are free and superb.
  • Sheldon Axler, Linear Algebra Done Right (3rd/4th ed.). The rigorous, determinant-light companion. Read it for the why behind the spectral theorem (Track D's orthogonal components) and the structure of operators on inner-product spaces (the foundation under Tracks B and E). The proofs you want to defend in your write-up are here in their cleanest form.
  • Stephen Boyd & Lieven Vandenberghe, Introduction to Applied Linear Algebra (VMLS). Free online. The most application-forward of the three, and the closest in spirit to this chapter — it treats least squares, data fitting, and matrix factorization as first-class topics. Excellent for the validation-and-presentation mindset.

Track A — SVD image compression

  • Strang, Introduction to Linear Algebra, the SVD chapter, for the A = UΣVᵀ geometry and the rank-one-layer decomposition.
  • Eckart & Young (1936), "The approximation of one matrix by another of lower rank." The original low-rank-optimality result you validate in code. (Primary source; for a modern treatment see Golub & Van Loan below.) [verify]
  • Trefethen & Bau, Numerical Linear Algebra, Lectures 4–5. The SVD done carefully, including the geometry and the numerical computation — useful when you swap in your from-scratch svd_from_scratch.

Track B — Recommender (matrix factorization)

  • Koren, Bell & Volinsky (2009), "Matrix Factorization Techniques for Recommender Systems," IEEE Computer. The accessible, canonical account of the method behind the Netflix Prize — exactly the gradient route in your demo, including regularization and why you fit only observed entries. [verify]
  • Boyd & Vandenberghe, VMLS, chapters on least squares and data fitting, for the optimization view of factorization.
  • The Eckart–Young connection (Track A references) — read alongside, because the SVD route (svd_complete) makes the low-rank link explicit.

Track C — PageRank

  • Page, Brin, Motwani & Winograd (1999), "The PageRank Citation Ranking: Bringing Order to the Web," Stanford technical report. The original. Read it for the random-surfer model and the role of damping. [verify]
  • Langville & Meyer, Google's PageRank and Beyond (2006). The definitive book-length treatment: the Google matrix, dangling nodes (your case-study fix), convergence of power iteration, and the Perron–Frobenius theory. The single best source if PageRank is your track.
  • Strang's eigenvalue chapters, for power iteration and the Perron–Frobenius theorem in the context you met them (Chapter 29).

Track D — PCA

  • Hotelling (1933) and Pearson (1901), the founding papers of PCA — historical, but worth seeing the variance-maximization and best-fit-line views side by side. [verify]
  • Jolliffe & Cadima (2016), "Principal component analysis: a review and recent developments," Phil. Trans. R. Soc. A. A clear modern survey, including the SVD-versus-covariance computation and the scaling caveat your case study flags.
  • Boyd & Vandenberghe, VMLS, and Strang's SVD chapter, for the connection PCA = SVD of centered data.

Track E — 3D rendering pipeline

  • Marschner & Shirley, Fundamentals of Computer Graphics. The standard text; the chapters on transformation matrices, homogeneous coordinates, viewing, and projection are precisely the pipeline you build. The clearest source for why the 4th coordinate and the perspective divide work.
  • Foley, van Dam, et al., Computer Graphics: Principles and Practice. The classic reference for the full model → view → projection chain and the order-of-composition pitfalls.
  • Chapter 12 of this book (computer graphics) and Chapter 21 (orthogonal matrices and rotations) are your in-book anchors.

Numerical methods (validation, all tracks)

  • Golub & Van Loan, Matrix Computations (4th ed.). The encyclopedia of how these decompositions are actually computed and how errors propagate — the reference behind every "diagnose, don't hide the discrepancy" decision in §39.8.2.
  • Trefethen & Bau, Numerical Linear Algebra. Conditioning, stability, and floating point, presented with unusual clarity — the natural companion to Chapter 38 when a from-scratch result and numpy diverge.

Free, online, and toward your next project

  • MIT OCW 18.06 (Strang) and fast.ai / 3Blue1Brown's Essence of Linear Algebra for geometric reinforcement of the transformations view that runs through every track.
  • For scaling any track into a portfolio of larger efforts, see the data science projects collection, where the same SVD, PCA, and matrix-factorization ideas drive end-to-end pipelines.
  • For how these matrices end up inside modern AI systems — every neural-network layer is a matrix multiply followed by a nonlinearity — see the accessible treatment of how models work.