# Linear Algebra II — main notes review

Notes by Benjamin Smith, based on Che Tat Ng's Fall 2004 course. Source title: PMath 245 — Advanced Linear Algebra 2. Catalog title retained as Linear Algebra II.

The original 22-page PDF and LaTeX are preserved with revision IDs and SHA-256 checksums. Downloaded PDF bytes match Dropbox content hash `99555d4cdfa2ad76f655d4c8fe0b13759482ee4842bf51674f1856b5e78a4607`. No originals or Dropbox files were modified.

## Repairs

Six exact, occurrence-checked source substitutions affect only the conversion input: change the block matrix macro from text tabular to math array; normalize the two explicit block matrices; remove nested dollar delimiters from two macro arguments; and replace the xymatrix diagram with a MathML array containing the same four nodes, four arrow directions, and the original T and N labels. Pandoc omits array rules, so a checked MathML postprocess restores vertical/horizontal block dividers with cell borders. Matrix entries and block dividers were checked against PDF pages 9–11 and 20. The diagram was checked against PDF page 20. Its typography and arrow lengths differ from the PDF.

Chapter/section statement numbering follows the source counter resets, including the carried counter before the first section of Chapters 2–4. All 81 statement labels match the PDF: 79 via extracted text, with Lemma 2.3.3 and Lemma 4.0.6 checked visually on PDF pages 9 and 18. The emphasized remark heading remains emphasized. Existing labeled statement IDs are preserved. All four source references resolve to the reviewed numbers: equation (1.1), section 1.2, statement 1.2.3 and statement 4.0.4.

Automated source/output checks cover 5 chapters, 19 section headings, 6 subsection headings (including starred headings), 8 body footnotes and 1,153 MathML nodes. No Pandoc warnings, raw-TeX math fallbacks, MathML errors or unresolved references remain. Text after end{document} and comments are excluded from source counts. The original author thanks is in the source preamble; the reading-page credits/contact preserve its attribution and correction address, while the body footnote count excludes it.

## Limits

This is a sampled conversion review, not an exhaustive mathematical audit. Existing source errors are retained: for example the singularity criterion and the prose calling a corollary a lemma. The chapter numbering and wording follow the historical source, and the original PDF remains available. HTML does not reproduce pagination, small-matrix sizing or exact typography. Supplementary course files and mobile review remain on the import ticket.