Appendix I — Mapping to Axler and to Boyd & Vandenberghe

This appendix maps our 40 chapters to two further classics that this book is in conversation with, each representing a different philosophy:

• Sheldon Axler, Linear Algebra Done Right (Springer; the 4th edition is freely readable online). The rigorous, proof-first counterpart. Axler develops the entire subject through linear maps on abstract vector spaces and famously delays determinants to the very last chapter, deriving eigenvalue theory without them.
• Stephen Boyd & Lieven Vandenberghe, Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares (Cambridge; free PDF at vmls-book.stanford.edu, hence "VMLS"). The applied counterpart — organized around vectors, matrices, and least squares, with worked examples from data fitting, control, and machine learning, and almost no abstract proof.

Because these books are organized so differently from ours, the mappings are topic-level, and many are approximate — flagged [verify]. Axler's section structure in particular was reorganized between the 3rd and 4th editions; confirm against your copy.

I.1 The two ordering philosophies to keep in mind

Before the table, the two structural facts that drive most of the mismatches:

• Axler is determinant-last and proof-first. He treats eigenvalues, the spectral theorem, and operator theory before determinants, which appear only in his final chapter (with the trace). This is the opposite of both this book (determinants in Part II) and Strang (determinants in the middle). An Axler-aligned reader should expect our Chapter 11 to have no early counterpart in Axler, and our eigenvalue chapters (23–28) to be where Axler's core lives.
• Boyd is applied and least-squares-centric. VMLS has three parts — Vectors (chs. 1–5), Matrices (chs. 6–11), and Least Squares (chs. 12–19) — and deliberately omits determinants, eigenvalues, the SVD, and abstract vector spaces to stay focused on what a data/engineering practitioner uses most. So several of our later chapters have no Boyd counterpart at all, marked "—".

I.2 Chapter-by-chapter correspondence

I.3 How to use each book alongside this one

If you are a math major reading Axler in parallel: treat our geometry-first chapters as the intuition layer beneath Axler's proofs. Our Chapters 5, 7, and 35 (vector spaces, matrices-as-maps, abstract transformations) are the on-ramps to his Chapters 1–3; our Chapters 23–28 line up with his eigenvalue and spectral-theorem core (Axler's Chapters 5–7); and his determinant-last philosophy means you should read our Chapter 11 as a geometric account he deliberately postpones. Axler's payoff — that you can do eigenvalue theory without determinants — is visible in how little our eigenvalue chapters actually lean on Chapter 11.

If you are a CS/data-science reader keeping Boyd open for applications: VMLS is the best companion for the applied chapters — Chapter 17 (regression), Chapters 18–20 (orthogonality and least squares), and Chapter 33 (machine learning) map directly onto its least-squares core (VMLS Parts II–III). But VMLS deliberately stops short of determinants, eigenvalues, the SVD, and abstract spaces — so for Chapters 11 and 23–36 you will want Strang (Appendix H) or this book alone. Think of Boyd as the deep, practical treatment of half this book — the half a practitioner uses daily — done with exceptional clarity.

A note on honesty in this table. Where a cell says "not covered" or "—," that is a real scope difference, not an oversight: Axler omits applications and numerics by design, and Boyd omits eigenvalues, the SVD, determinants, and abstraction by design. The [verify] flags mark places where the section-level fit depends on the edition or where a topic is present but not in a cleanly corresponding unit. Trust the topic names over the structure.