🌐 [translation-sync] TEST: Display math equations changed (13 - lecture)

[mmcky]

Automated Translation Sync

This PR contains automated translations from QuantEcon/test-translation-sync.

Source PR

#989 - TEST: Display math equations changed (13 - lecture)

Files Added

• ✅ .translate/state/lecture.md.yml

Files Updated

• ✏️ lecture.md

Details

• Source Language: en
• Target Language: ml
• Model: claude-sonnet-5

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This PR was created automatically by the translation action.

[github-actions]

✅ Translation Quality Review

Verdict: PASS | Model: claude-sonnet-5 | Date: 2026-10-09
Routing: editor — 2 minor finding(s) in gating categories (accuracy/terminology/syntax/diff-check/other)

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📝 Translation Quality

Criterion	Score
Accuracy	9/10
Fluency	8/10
Terminology	9/10
Formatting	10/10
Overall	8.9/10

Summary: The translation of the changed sections (Vector Spaces, Applications in Economics, Matrix Operations, Eigenvalues and Eigenvectors) is accurate, fluent, and terminologically consistent with the glossary and style policy. Minor issues include one translated code comment that should have remained in English per policy, and a translated print string that creates inconsistency with sibling English print strings in the same cell. No blocking or major issues were found; mathematical content and code structure are fully intact. Consistent and correct application of the English-retention glossary for technical terms (vector, matrix, eigenvalue, eigenvector, Leontief inverse, etc.) Mathematical notation and LaTeX blocks preserved exactly without alteration Code blocks and structure preserved correctly, with proper fencing and MyST directive syntax maintained Correct use of hortative forms (നമുക്ക് ... ചെയ്യാം) in instructional sentences matching the style policy Comma placement after fronted clauses and topic markers largely follows the specified policy

Suggestions:

• [minor · fluency] lecture.md — ## Vector Spaces, opening sentence: The phrase 'vector space എന്നത് ... ഒരു collection ആണ്' is accurate but slightly literal; a comma after the topic marker എന്നത് is correctly applied per the policy, so this is fine. However 'ഇവ പരസ്പരം add ചെയ്യാനും scalars കൊണ്ട് multiply ചെയ്യാനും കഴിയും' reads slightly awkward with 'scalars കൊണ്ട്' — 'scalars ഉപയോഗിച്ച്' would flow more naturally in this register. → ഇവ പരസ്പരം add ചെയ്യാനും scalars ഉപയോഗിച്ച് multiply ചെയ്യാനും കഴിയും
• [minor · terminology] lecture.md — ## Matrix Operations, code comment translation: The English code comment '# Final demand vector (in billions)' was translated to '# Final demand vector (billions-ൽ)', but the policy states code comments should never be translated and must stay exactly as in the source. → # Final demand vector (in billions)
• [minor · terminology] lecture.md — code cell under Matrix Operations, print statement: The print string '"Total Output Required (billions):"' was translated to '"ആവശ്യമായ Total Output (billions):"'. This is a user-facing string, not a comment, so translating it is a judgment call, but it changes the printed output language inconsistently with the rest of the untouched print strings (e.g., 'Input-Output Matrix:', 'Leontief Inverse:') which remain English. This creates inconsistency … → Keep as "Total Output Required (billions):" to match the English-only print strings elsewhere in the same cell, or translate all print strings consistently.
• [nit · fluency] lecture.md — ## Eigenvalues and Eigenvectors, 'growth theory മുതൽ stability analysis വരെ': Minor stylistic point: the clause order mirrors English fairly closely; a more natural Malayalam ordering could front the main clause after the adverbial phrase, though a comma already separates them correctly.

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🔍 Diff Quality

Check	Status
Scope Correct	✅
Position Correct	✅
Structure Preserved	✅
Heading-map Correct	✅
Overall	10/10

Summary: All five math expression additions (∈ ℝⁿ, ∈ ℝ^(m×n), eigenvalue equation nonzero condition, λ∈ℂ, and v₀≠0 condition) were correctly mirrored in the target document at matching positions with no heading text changes requiring heading-map updates.

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This review was generated automatically by action-translation review mode.

[Copilot]

🟢 Approval recommended

The LaTeX math edits are correct and language-independent, and the state file metadata (including section-count of 3 matching the three level-2 headings) is fully consistent with the source PR.

0 open findings

What changed in this PR

This is an automated translation-sync PR that propagates upstream changes from QuantEcon/test-translation-sync#989 into the Malayalam (ml) translation. The upstream source added mathematical qualifiers to several display-math equations in the "Linear Algebra Foundations" lecture, and this PR mirrors those LaTeX changes into the translated lecture.md while recording the sync state.

Changes:

• Added explicit set-membership / constraint annotations to five display equations in lecture.md (e.g., \in \mathbb{R}^n, \in \mathbb{R}^{m \times n}, \lambda \in \mathbb{C}, \mathbf{v} \neq \mathbf{0}) and switched the eigenvalue equation to bold-vector notation (A\mathbf{v} = \lambda \mathbf{v}).
• Added a new translation-state file .translate/state/lecture.md.yml capturing the sync metadata.

File	Description
lecture.md	Mirrors upstream LaTeX changes adding math constraints to display equations; all edits are language-independent and mathematically correct.
.translate/​state/​lecture.md.yml	New sync-state record; source-sha, synced-at, model, mode=UPDATE, tool-version, and section-count: 3 are all consistent with the PR metadata and file contents.

🧠 Review effort: Balanced

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[mmcky]

Closing for test reset