cross_product_trick#

  • Series: lecture-dp

  • File: lectures/cross_product_trick.md

  • Audit date: 2026-05-28

  • Categories audited: writing, math, code, jax, figures, references, links, admonitions

  • Overall score: 5.7 / 10

  • Priority: HIGH

Score breakdown#

Category

Score

One-line note

Writing

6/10

Title-Case H2 headings, i.i.d. used, several multi-sentence paragraphs.

Math

3/10

Apostrophe transpose universal; bare align* outside $$; broken {eq} ref.

Code

N/A

Single empty code cell — effectively no code content.

JAX

out of scope

not a JAX lecture.

Figures

N/A

No figures.

References

N/A

No citations.

Links

8/10

Single {doc} reference, used correctly.

Admonitions

N/A

No admonitions.

Issues#

Critical#

  • [qe-math-013 (proposed)] — Broken equation reference: {eq}eq:Kalman102}has a closing}instead of a backtick (line 133). The label(eq:Kalman102)is also attached to a barealign*block (line 121) rather than a numbered$\( … \)$` block, so the label won’t bind even if the syntax is fixed. Build risk: will render as raw text.

High severity#

  • [qe-math-002] — Apostrophe ' used as transpose throughout (e.g. x_t' R x_t, B'PB, A'PA, D \Sigma_t D'). Lines: 48, 63, 68, 119-121, 142, 164-167. Count: 30+ occurrences.

  • [qe-math-006] — Bare \begin{align*} … \end{align*} blocks (not wrapped in $$) appear in five places. Lines: 82-88, 104-107, 118-121, 126-129, 140-143. These should be $$ \begin{aligned} … \end{aligned} $$ to render correctly in PDF.

Medium severity#

  • [qe-writing-006] — H2 headings use Title Case. Examples: ## Undiscounted Dynamic Programming Problem (line 33), ## Kalman Filter (line 92).

  • [qe-writing-009 (proposed)] — i.i.d. used in narrative (line 110). Should be IID.

Low severity#

  • [qe-writing-001] — Several multi-sentence paragraphs (e.g. 80-89, 94-95, 145-151).

  • [qe-writing-005] — “duality” used for emphasis but is not a definition (line 94); reserve bold for definitions.

Strengths#

  • Lecture title in Title Case.

  • Math symbols (\(P\), \(R\), \(Q\)) use plain letters consistent with qe-writing-004.

  • Cross-reference {doc}Linear Control: Foundations `` used correctly.