[action-translation] resync: svd_intro.md

[mmcky]

Forward Resync: svd_intro.md

Source: QuantEcon/lecture-python.myst — lectures/svd_intro.md
Source commit: 388b273
This PR resyncs the translation to match the current source document.

Reason: Target adds font configuration code (matplotlib font setup) not in source (minor i18n code, acceptable), but more importantly TARGET contains substantive additional content not in SOURCE: e.g., extra explanatory sentence in PCA section ('SVD 是一种将矩阵分解为有用组件的方法...而 PCA 则是一种基于 SVD 的数据分析方法...'), an added sentence after Step 5 score matrix ('这个矩阵的每一列代表一个主成分...'), and expanded/rephrased 'Connections' section with additional explanatory sentences not present in SOURCE. Also SOURCE's Overview section mentions DMD comparison to PCA which is missing in TARGET's overview (content changes), and the Eckart-Young Wikipedia link target differs (zhihu vs wikipedia), and pseudoinverse Wikipedia link changed to Baidu Baike link - these are different URL targets (CONTENT_CHANGES), but combined with clear additions, TARGET_HAS_ADDITIONS takes priority.

Changes

Whole-file resync applied. The entire document was resynced in a single pass.

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Created by action-translation forward resync

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[Copilot]

Pull request overview

This PR forward-resyncs the Chinese translation of lectures/svd_intro.md to match the latest upstream source (QuantEcon/lecture-python.myst @ 388b2735...), and records the sync state for automation.

Changes:

• Added translation: frontmatter metadata (title + heading mappings) to lectures/svd_intro.md.
• Resynced/rewrote multiple paragraphs and section phrasing to align with the upstream lecture (including updated external links).
• Added .translate/state/svd_intro.md.yml to track the synced source SHA, date, model, and section count.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.

File	Description
lectures/svd_intro.md	Resynced translated lecture content and added translation frontmatter metadata.
.translate/state/svd_intro.md.yml	Added translation sync state metadata (source SHA, synced date, tool/model info).

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[github-actions]

🚀 Deployed on https://6a5c52e56657f1cd87b5de2f--astonishing-narwhal-a8fc64.netlify.app

[github-actions]

✅ Translation Quality Review

Verdict: PASS | Model: claude-sonnet-5 | Date: 2026-07-19

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📝 Translation Quality

Criterion	Score
Accuracy	8/10
Fluency	8/10
Terminology	8/10
Formatting	7/10
Overall	7.9/10

Summary: This is a solid whole-file resync translation that accurately conveys the technical content of the SVD lecture, preserving nearly all mathematical formatting and maintaining consistent terminology per the glossary. Minor issues include an unexplained addition of font-loading code in one code cell, some paraphrasing in the Overview section that diverges slightly from the source's precise wording, and occasional awkward sentence splits in the Four Fundamental Subspaces section. No critical syntax errors were found; headings, code blocks, and math delimiters are all properly formatted. Mathematical notation, LaTeX equations, and equation labels are accurately preserved throughout the resynced document Core technical terminology (奇异值分解, 特征向量, 正交矩阵, 主成分分析, etc.) is applied consistently and matches the reference glossary Code blocks are correctly preserved with appropriate translation of comments and print statements into natural Chinese Complex mathematical explanations (Eckart-Young theorem, polar decomposition, PCA-SVD relationship) are rendered clearly and accurately

Suggestions:

• Code cell after '让我们看一个例子。': the translation adds font-loading code (FONTPATH, mpl.font_manager, plt.rcParams) not present in the English source; this is an unexplained addition to a code block that should either be documented as a standard localization pattern or removed to match source exactly
• '四个基本子空间' section: '让$u_i, i = 1, \ldots, m$为$U$的$m$个列向量，令' is awkwardly split across two lines with 'let' translated separately mid-sentence, disrupting flow — consider merging into a single fluent sentence like '设$u_i, i=1,\ldots,m$为$U$的$m$个列向量，$v_i, i=1,\ldots,n$为$V$的$n$个列向量'
• Overview section translation is a loose paraphrase rather than a direct translation: 'SVD是一个强大的数学工具...它不仅可以用于最小二乘投影，还是许多统计和机器学习方法的基石' significantly restructures and adds interpretive content (e.g., 'in data analysis and machine learning has broad applications') not explicit in the English source, which more narrowly states SVD is 'a work-horse in applications of least squares projection that form foundations for many statistical and machine learning methods'
• '基本设定' section: '在实际应用中，$X$通常代表一个数据矩阵' is an added transitional phrase not present in the source text ('In much of this lecture, we'll think of $X$ as a matrix of data in which'), slightly altering emphasis from 'in this lecture' to 'in practical applications'
• Four Fundamental Subspaces section: bullet list definitions (列空间/零空间/行空间/左零空间) compress multiple sentences into single lines losing the 'i.e.,' explanatory clause structure — e.g., '零空间$X$，记作${\mathcal N}(X)$，包含所有满足$Xy=0$的向量$y$' omits the source's explicit phrasing pattern, though meaning is preserved

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🔍 Diff Quality

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

Summary: The target document was correctly resynced to match the current English source, with all sections, code cells, equations, and structure preserved in the same order, and the translation frontmatter heading map accurately added and aligned with body headings.

Issues:

• The 'PCA with Eigenvalues and Eigenvectors' heading translation changed from '基于特征值分解的PCA' to '基于特征值和特征向量的PCA' between before/after target, but the frontmatter heading map correctly reflects the updated translation, consistent with body content.
• One footnote link target changed (zhihu.com -> wikipedia.org, baidu.com -> wikipedia.org) matching the English source's links, which is a correct resync fix rather than an error.

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