Appendix H — Mapping to Strang's Introduction to Linear Algebra

This appendix is for instructors (and self-studiers) who are switching between this book and Gilbert Strang's Introduction to Linear Algebra (Wellesley–Cambridge Press), the closest spiritual sibling to this text and the source of the "four fundamental subspaces" framing we adopt in Part III. The two books share a worldview — linear algebra as something you see and do, with the column picture of $A\mathbf{x}$ front and center — so the mapping is unusually clean.

A caution about precision. Strang's book has gone through several editions (the 5th and 6th are the most common in classrooms), and section numbers move between editions. For that reason this table maps to Strang's chapters and named topics, not to exact section numbers; where even the chapter-level fit is loose, it is flagged [verify]. Use the topic names, not the numerals, to find the corresponding material in whichever edition you hold. Strang's chapter numbering used below follows the widely circulated structure (Ch. 1 Vectors → Ch. 10 Applications); confirm against your copy.

H.1 Chapter-by-chapter correspondence

H.2 The two big ordering differences

If you are migrating a Strang-based syllabus to this book (or vice versa), two structural differences matter more than any individual row above:

1. Transformations come early here, late in Strang. We introduce "a matrix is a function" in Chapter 7 — the gateway to the entire middle of the book — whereas Strang develops the four subspaces first and treats linear transformations formally in his Chapter 8. An instructor who likes Strang's order can read our Chapter 7 as a preview and our Chapter 35 as the formal payoff; an instructor who likes our order can pull Strang's Chapter 8 forward.

2. Determinants come early here, late in Strang. We place the determinant in Part II (Chapter 11) as the area/volume-scaling factor, tightly coupled to the transformation picture. Strang famously places determinants in his Chapter 5, after the four fundamental subspaces, on the view that they are less central than students assume. (This is the opposite of Axler, who defers determinants to the very end — see Appendix I.) Both choices are defensible; ours is driven by the geometry.

H.3 What the two books share most strongly

The four-fundamental-subspaces framework of our Part III is, more than anything else, the inheritance from Strang: the picture of $C(A)$, $N(A)$, $C(A^{\mathsf{T}})$, and $N(A^{\mathsf{T}})$ as the organizing skeleton of the whole subject — and the locked notation we use for them (Appendix F) — is his. For that material the two books are nearly interchangeable, down to the symbols. Strang's MIT OpenCourseWare lectures (18.06) follow his book closely and pair well with either text; his "big picture of linear algebra" diagram is the visual our Chapters 13–14 build toward.