Linear Algebra: Reading Guide
Start with the lessons, then use Strang's Linear Algebra and Its Applications
index
for one named gap. The local extraction identifies Gilbert Strang; these are
chunk locators in Books/Linear Algebra and Its Applications/contents/README.md,
not guaranteed section numbering in every edition. Some OCR formulas need checking
against the source PDF. The former repeated links to one chapter do not identify
all the topics their labels claimed.
| After | Local topic/locator | Read-to-produce output |
|---|---|---|
| Elimination | 1.3: 008–010; row exchanges/factors 015–016 | A solve invariant and permutation check |
| Spaces and bases | 2.1: 027–029; Ax=0/Ax=b 030–035; basis 036–039; four spaces 040 onward | Basis, nullspace and impossibility witness |
| Transformations | 2.6 topic in the index, including 051 | A coordinate-change derivation |
| Projection and QR | 3.3: 060–062; 3.4 orthogonal bases/Gram-Schmidt, including 067 | Pythagorean least-squares proof and factor check |
| Spectra | Chapter 5: eigenvalues, diagonalization and similarity | A valid eigenbasis or a counterexample |
| Positive structure | 6.2: 114–118 | PD proof plus a PSD boundary counterexample |
| SVD | 6.3: 119–121 | Two approximation errors and explicit factor shapes |
| Numerical judgment | 7.2: 128–129; 7.4: 133–135 | Perturbation bound and convergence assumptions |
Read a bounded section, close it, reconstruct one argument and solve a changed instance. Full-book reading has its own budget on the full-book path.
Optional depth with a deliverable
- MIT 18.06SC SVD lesson: use the worked teaching material to explain input and output singular directions.
- Higham on elimination growth: distinguish bounded multipliers from growth of intermediate entries; write the missing hypothesis in an overly strong stability claim.
- LAPACK least-squares error analysis: advanced reading on why backward stability and forward sensitivity are distinct. It is not an extra prerequisite for the exact small examples.
- Local
Resources/pdfs/contains Linear Algebra by Jim Hefferon, fourth edition; Linear Algebra Abridged by Sheldon Axler (2016); and Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra. These are located inventory candidates, not fully audited assignments. Verify edition and contents, then choose one proof exercise or algorithmic application addressing a named gap. Do not add all three as simultaneous required books.
The upgrade inspected selected local material and targeted primary web sources; it did not audit the complete Books, reading or Resources collections.