[action-translation] resync: eig_circulant.md

[mmcky]

Forward Resync: eig_circulant.md

Source: QuantEcon/lecture-python.myst — lectures/eig_circulant.md
Source commit: 6a512f1
This PR resyncs the translation to match the current source document.

Reason: Several substantive omissions and alterations exist in the target: missing intro sentence about circulant matrices' connection to convolution and eigenvectors via DFT and cross-reference links to linear_algebra and hoist_failure docs; missing 'For background...' sentence; summation index changed from N-1 to n-1 in convolution formula (inconsistent with source); det formula rendered differently (missing parentheses/minus sign nuance, though minor); C^T rendered as C^T vs C' inconsistently; PP^T changed to PP' notation; missing explicit mention 'Suppose A and B are circulant matrices of same order and same cyclic shift convention' (simplified); code renamed (construct_circulant -> construct_cirlulant, DFT function inverse_DFT -> inverse_transform, added @jit decorators and numba import, added font-loading code) - font/jit are i18n/tooling but inverse_DFT function rename and eigenvector printing Q[:, i] changed to Q[i, :] is a functional discrepancy; formula for eigenvalue of C8 changed variable names and added extra clause 'where w^{k-1} is P8's corresponding eigenvalue' not in source; plot_magnitude X-axis label changed from 'k' to 'j'; overall multiple content-level formula/variable inconsistencies beyond mere style, requiring review against source.

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 the eig_circulant lecture to better match the upstream source document, updating both the mathematical exposition and the accompanying Python code cells, and recording resync state metadata.

Changes:

• Added translation frontmatter metadata and restored missing/updated explanatory text (including cross-references).
• Updated math notation and formulas (e.g., convolution index bounds, transpose notation, determinant expression).
• Renamed/standardized helper functions used in code cells (e.g., construct_circulant, construct_cyclic_shift_matrix, inverse_DFT) and adjusted related narrative.

Reviewed changes

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

File	Description
lectures/eig_circulant.md	Resynced lecture content, math, and code cells to match source; adds translation metadata and updates multiple formulas/names.
.translate/state/eig_circulant.md.yml	Records resync provenance (source SHA/date/model/mode).

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[github-actions]

✅ Translation Quality Review

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

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📝 Translation Quality

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

Summary: This is a high-quality translation that accurately and fluently conveys the technical content of the English source, with correct terminology usage throughout. The main concern is the unauthorized addition of extra code (numba import, matplotlib font configuration) in the first code cell that doesn't exist in the source document, which should be reviewed for consistency with translation policy. Minor stylistic improvements could be made to one or two sentences split around display equations, but overall the translation is faithful and well-executed. Excellent accuracy in translating complex mathematical definitions and explanations (e.g., circulant matrix definition, permutation matrix concepts, DFT formulas) Consistent and correct use of standard mathematical/linear algebra terminology (特征值, 特征向量, 置换矩阵, 循环矩阵, 卷积) matching the glossary All LaTeX equations, code blocks, and MyST directives (prf:definition, eq references) are correctly preserved Natural, fluent academic Chinese phrasing throughout, especially in explanatory passages about eigenvalues and roots of unity

Suggestions:

• Code import block: The translation added extra imports (from numba import jit, matplotlib as mpl, font configuration lines) that are not present in the English source. These should be removed to maintain fidelity to the original document unless this is a standard project-wide convention applied consistently across all translated lectures.
• 构造循环矩阵 section, 'circulant shift' explanation: '是一个循环移位算子' - the English says 'serves as a cyclic shift operator' which is accurately translated, but consider verifying 'h' variable reference is preserved correctly (it is, this is fine).
• P的特征向量部分: '对于系数向量 ${c_i}_{i=0}^{n-1}$，$P$ 的特征向量也是 ... 的特征向量' - this splits the sentence awkwardly around the display equation which slightly disrupts the natural flow compared to the source's single-sentence structure; consider rephrasing as '对于系数向量...，P的特征向量同样是如下矩阵的特征向量：' for smoother reading.

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🔍 Diff Quality

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

Summary: The resync correctly re-aligned the Chinese translation to match the current English source structure, content, and heading metadata.

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