🌐 [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: fa
• 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 — 1 minor finding(s) in gating categories (accuracy/terminology/syntax/diff-check/other)

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📝 Translation Quality

Criterion	Score
Accuracy	9/10
Fluency	9/10
Terminology	9/10
Formatting	10/10
Overall	9.2/10

Summary: The translation of the modified sections (Vector Spaces, Applications in Economics, Matrix Operations, Eigenvalues and Eigenvectors) is accurate, fluent, and terminologically consistent with the glossary. Mathematical formatting and code blocks are fully preserved with no syntax errors. Minor stylistic improvements are possible in a couple of sentences, but these do not impede comprehension or correctness. Mathematical notation, LaTeX equations, and code blocks are preserved perfectly across all modified sections Economic and linear algebra terminology (e.g., معکوس لئونتیف, ماتریس انتقال, مقادیر ویژه, فضای برداری) is consistent with the glossary and domain conventions Code comments are naturally and accurately translated into Persian while preserving code functionality Overall sentence structure maintains formal academic register appropriate for an economics/math lecture

Suggestions:

• [minor · terminology] lecture.md — ## Eigenvalues and Eigenvectors - 'برای یک ماتریس $n \times n$ به نام $A$': The phrase 'به نام A' (meaning 'named A') is an awkward addition not present in the English source ('For an n×n matrix A'). A more natural and direct rendering would simply attach the symbol to the noun phrase. → برای ماتریس $n \times n$ با نام $A$، یا ساده‌تر: «برای یک ماتریس $A$ با ابعاد $n \times n$، چندجمله‌ای مشخصه عبارت است از:»
• [minor · fluency] lecture.md — #### Applications in Economics (Vector Spaces): The sentence 'ویژگی بسته بودن تضمین می‌کند که ترکیب‌های تخصیص‌های امکان‌پذیر، امکان‌پذیر باقی می‌مانند' is slightly repetitive/clunky due to repeating 'امکان‌پذیر' twice in close proximity, though it is accurate. A smoother phrasing could improve readability. → ویژگی بسته بودن تضمین می‌کند که ترکیب تخصیص‌های شدنی، همچنان شدنی باقی می‌ماند
• [nit · terminology] lecture.md — ## Matrix Operations - 'حاصل‌ضرب $AB$ نشان‌دهنده اعمال تبدیل $B$ و سپس تبدیل $A$ است': Translation is accurate and clear; just noting 'اعمال' (applying) combined with 'و سپس' reads naturally, no change needed — flagged only as a very minor stylistic note that 'به‌کارگیری' could also be used, but current choice is fine.

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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, ∈ ℝᵐˣⁿ, and the three equation qualifiers) were correctly translated and positioned in matching locations within lecture.md, with structure and heading map unaffected.

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

[Copilot]

🟢 Approval recommended

The translated math equations match the English source exactly and the state metadata is internally consistent and correct.

0 open findings

What changed in this PR

This is an automated translation-sync PR that propagates upstream changes from the English source repository (QuantEcon/test-translation-sync PR #989) into the Farsi (fa) translation. The source change refines the display math equations in the "Linear Algebra Foundations" lecture, adding set/membership annotations (e.g., \in \mathbb{R}^n) and tightening the eigenvalue notation. Since LaTeX math is language-independent, the Farsi file mirrors these equation updates verbatim while leaving the surrounding translated prose unchanged.

Changes:

• Update six display-math equations in lecture.md to match the upstream source (vector/matrix membership annotations, bold eigenvector notation, and non-zero/complex-domain qualifiers).
• Add the per-file translation state record .translate/state/lecture.md.yml tracking source SHA, sync date, model, mode, section count, and tool version.

File	Description
lecture.md	Updates display math equations to exactly match the English source equations.
.translate/​state/​lecture.md.yml	Adds sync metadata (mode UPDATE, section-count 3, source-sha, synced-at, model, tool-version).

I verified each of the six equation edits against the English source at commit 7e14b74, and they match exactly. The state metadata is internally consistent: source-sha matches the PR's sourceCommitSha, section-count: 3 matches the three top-level translation.headings entries, synced-at: "2026-10-09" is today's date (not a future date), and mode: UPDATE is consistent with lecture.md being an updated file. No issues were found.

🧠 Review effort: Balanced

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[mmcky]

Closing for test reset