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Copilot AI commented Dec 19, 2025

Issue "Jordan form of a proof" with instruction "A discrete option" interpreted as request for mathematical proof documentation in discrete mathematics context.

If this pull request (PR) pertains to Chinese-to-English translation, please confirm that you have read the contribution guidelines and complete the checklist below:

  • This PR represents the translation of a single, complete document, or contains only bug fixes.
  • The translation accurately conveys the original meaning and intent of the Chinese version. If deviations exist, I have provided explanatory comments to clarify the reasons.

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Changes

New appendix section 16.4 covering proof techniques used in algorithm analysis:

Core Content

  • Direct proof, contradiction, induction, constructive proof with examples
  • Algorithm correctness proofs (greedy choice property, dynamic programming)
  • Jordan normal form as advanced topic with applications to graph adjacency matrices and Markov chains

Files Added

  • docs/chapter_appendix/proof_techniques.md (中文)
  • en/docs/chapter_appendix/proof_techniques.md (English)
  • zh-hant/docs/chapter_appendix/proof_techniques.md (繁體中文)
  • ja/docs/chapter_appendix/proof_techniques.md (日本語)

Navigation

Updated all four mkdocs.yml files to include new section in appendix chapter.

Discrete Context Note

Explicitly addresses "discrete option" requirement by positioning Jordan normal form within discrete mathematics applications (graph spectral analysis, Markov chain analysis) rather than continuous mathematics.

Original prompt

This section details on the original issue you should resolve

<issue_title>Jordan form of a proof.</issue_title>
<issue_description></issue_description>

<agent_instructions>A discrete option.</agent_instructions>

Comments on the Issue (you are @copilot in this section)


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Copilot AI self-assigned this Dec 19, 2025
Copilot AI and others added 2 commits December 19, 2025 06:43
…al form

Co-authored-by: ewdlop <25368970+ewdlop@users.noreply.github.com>
…s documentation

Co-authored-by: ewdlop <25368970+ewdlop@users.noreply.github.com>
Copilot AI changed the title [WIP] Fix issue related to Jordan form of a proof Add mathematical proof techniques documentation including Jordan normal form Dec 19, 2025
Copilot AI requested a review from ewdlop December 19, 2025 06:47
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Jordan form of a proof.

2 participants