🌐 [translation-sync] [linear_algebra] Some updates on code and style and typos

[mmcky]

Automated Translation Sync

This PR contains automated translations from QuantEcon/lecture-python.myst.

Source PR

#1054 - [linear_algebra] Some updates on code and style and typos

Files Updated

• ✏️ lectures/linear_algebra.md
• ✏️ .translate/state/linear_algebra.md.yml

Details

• Source Language: en
• Target Language: zh-cn
• Model: claude-sonnet-5

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This PR was created automatically by the translation action.

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✅ Translation Quality Review

Verdict: PASS | Model: claude-sonnet-5 | Date: 2026-09-12
Routing: editor — 1 minor finding(s) in gating categories (accuracy/terminology/syntax/diff-check/other)
Shadow gate: would NOT auto-merge (recorded only; no action taken)

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📝 Translation Quality

Criterion	Score
Accuracy	9/10
Fluency	8/10
Terminology	9/10
Formatting	8/10
Overall	8.6/10

Summary: This is a strong, accurate translation of a technically dense linear algebra lecture. Mathematical content, code, and formatting are well preserved, and terminology aligns closely with the provided glossary. Minor issues include a few overly free rephrasings in the Overview section that slightly shift emphasis, an unexplained kernel tag change in a couple of code cells, and a couple of mildly awkward sentence constructions. None of these rise to the level of blocking or major accuracy issues. Mathematical notation, LaTeX equations, and code blocks are faithfully preserved throughout the changed sections Technical terminology (特征值, 特征向量, 线性无关, 张成空间, 正定矩阵, etc.) is applied consistently and matches the glossary Full-width Chinese punctuation is used correctly throughout prose text Complex mathematical proofs in the exercise solution are translated with high fidelity to the original derivation steps

Suggestions:

• [minor · fluency] lectures/linear_algebra.md — ## Overview: The sentence 'This case is very important... 我们将同时关注理论基础和实际计算' splits a single English sentence into two Chinese sentences and adds a somewhat redundant restructuring compared to source, plus the next sentence about overlap with numpy is rephrased quite freely ('虽然本讲与...有所重合，但这里我们将从更理论的角度来探讨线性代数') which changes the original meaning (source says lecture admits overlap with numpy doc, not that it t… → 本讲将介绍线性代数和矩阵运算的基础知识，涵盖理论与计算两个方面。我们承认这与 {doc}programming:numpy 中已经介绍过的NumPy数组操作有一定重合。
• [minor · formatting] lectures/linear_algebra.md — ```{code-cell} ipython (imports): The translation's import code cell adds extra lines (matplotlib font configuration, figure size) not present in the English source. While this may be intentional for CJK font rendering in the translated notebook, it is a deviation from the source content that should be flagged since it changes the code block content beyond translation. → If this is a standard practice across translated lectures for CJK font support, no change needed; otherwise align code cell with the source content.
• [minor · terminology] lectures/linear_algebra.md — 特征值和特征向量 section, eig code cell: The tag for the eigenvector plot code cell was changed from {code-cell} python3 to {code-cell} ipython3 (and similarly for the subsequent eig computation cell), which is an unexplained deviation from the source's kernel tag and not part of translation scope. → Keep {code-cell} python3 consistent with the English source unless there is a documented reason for the change.
• [minor · fluency] lectures/linear_algebra.md — ### 矩阵运算: The phrase '并且其设计使得乘法能够很好地配合基本线性运算' is a separate sentence, splitting what was one sentence in English ('and is designed to make multiplication play well with basic linear operations'). This is a minor stylistic choice, not an error, but creates slightly choppier flow than necessary. → 矩阵乘法的规则推广了上面讨论的内积概念，并且其设计使得乘法能够很好地配合基本线性运算。
• [nit · fluency] lectures/linear_algebra.md — ### NumPy中的矩阵: '由于运算默认按元素执行，标量乘法和加法的语法具有非常自然' is grammatically incomplete — missing a predicate noun after '非常自然' (e.g., '自然的语法' or '...非常自然'). → 由于运算默认按元素执行，标量乘法和加法的语法非常自然。

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🔍 Diff Quality

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

Summary: The translation sync correctly mirrors all source changes in the same positions, preserves document structure, and accurately updates the heading map keys to match the new English heading casing.

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

[Copilot]

🟡 Changes recommended

New {doc} / {ref} intersphinx references use an unmapped programming: prefix (repo config uses pyprog), likely causing unresolved references during documentation builds.

Get a fresh assessment by requesting another Copilot review.

Pull request overview

This PR syncs the Chinese translation of the Linear Algebra lecture with upstream changes, updating section metadata, cross-references, and several code/math/style elements to match the source content.

Changes:

• Updates translation.headings keys and multiple math expressions (notably switching transpose notation to ^\top).
• Refactors several plotting code cells (axis drawing and figure sizing) and standardizes some code-cell directives.
• Replaces some external links with intersphinx-style {doc} / {ref} cross-references and updates translation sync state metadata.

File summaries

File	Description
lectures/linear_algebra.md	Main lecture sync: heading metadata, math notation updates, plotting/code-cell tweaks, and link/reference changes
.translate/state/linear_algebra.md.yml	Updates translation sync state (source SHA, date, mode, tool version)

Review details

Suppressed comments (2)

lectures/linear_algebra.md:239

• 这里的 intersphinx 引用使用了 programming: 前缀，但仓库 lectures/_config.yml 里指向 python-programming.quantecon.org 的映射键名是 pyprog。如果前缀不匹配，{ref} 会解析失败。建议将 programming: 改为 pyprog:。

在Python中，向量可以用列表或元组来表示，例如 `x = (2, 4, 6)`，但更常见的是用 {ref}`NumPy数组 <programming:numpy_array>` 来表示。

lectures/linear_algebra.md:635

• 这两处 {ref} 使用了 programming: 前缀，但 lectures/_config.yml 中 intersphinx 映射到 python-programming.quantecon.org 的键名是 pyprog。前缀不一致会导致引用解析失败。建议将 programming: 改为 pyprog:。

`shape` 属性是一个表示行数和列数的元组 --- 更多讨论请参见 {ref}`这里 <programming:numpy_shape_dim>`。

要获取 `A` 的转置，可以使用 `A.transpose()` 或更简单的 `A.T`。

有许多便捷的函数可用于创建常见矩阵（零矩阵、全1矩阵等）--- 参见 {ref}`这里 <programming:creating_arrays>`。

• Files reviewed: 2/2 changed files
• Comments generated: 1
• Review effort level: Lite

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