[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6NVECPD231D066AYFCVVDGT":3,"skill-same:01M6NVECPD231D066AYFCVVDGT":60},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":18,"publishedAt":31,"linkOnly":32,"markdownContent":33,"markdownBody":34,"frontMatter":35,"refName":38,"commitSha":39,"skillDirectory":40,"forksCount":14,"repositoryHtmlUrl":41,"repositoryHomepageUrl":6,"ownerHtmlUrl":42,"ownerBlogUrl":43,"ownerDescription":44,"updatedAt":45,"install":46,"resources":59},"01M6NVECPD231D066AYFCVVDGT","vector-spaces",null,"Problem-solving strategies for vector spaces in linear algebra","rubicanjr\u002FFinCognis","rubicanjr","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F234912519?v=4","01M6NT156NND8J474G34SB3923","Rubi","01M6NT15B70RWXE1N3YV0BZY8A",0,"MIT","https:\u002F\u002Fgithub.com\u002Frubicanjr\u002FFinCognis\u002Fblob\u002Fmain\u002Fskills\u002Fmath\u002Flinear-algebra\u002Fvector-spaces\u002FSKILL.md",[],[19,20,21,22,23,24,25,26,27,28,29,30],"vector","spaces","vector spaces","linear","Bash","read","problem-solving","strategies","algebra","linear algebra","problem","for","2026-11-10 10:12:30",false,"---\nname: vector-spaces\ndescription: \"Problem-solving strategies for vector spaces in linear algebra\"\nallowed-tools: [Bash, Read]\n---\n\n# Vector Spaces\n\n## When to Use\n\nUse this skill when working on vector-spaces problems in linear algebra.\n\n## Decision Tree\n\n\n1. **Check Subspace**\n   - Contains zero vector?\n   - Closed under addition?\n   - Closed under scalar multiplication?\n   - Verify with `z3_solve.py prove`\n\n2. **Linear Independence**\n   - Set up Ax = 0 where columns are vectors\n   - `sympy_compute.py nullspace \"A\"`\n   - Trivial nullspace = independent\n\n3. **Basis and Dimension**\n   - Find spanning set, remove dependent vectors\n   - `sympy_compute.py rref \"A\"` to find pivot columns\n   - Dimension = number of pivots\n\n4. **Change of Basis**\n   - Find transition matrix P\n   - New coords = P^(-1) * old coords\n   - `sympy_compute.py inverse \"P\"`\n\n\n## Tool Commands\n\n### Sympy_Nullspace\n```bash\nuv run python -m runtime.harness scripts\u002Fsympy_compute.py nullspace \"[[1,2,3],[4,5,6]]\"\n```\n\n### Sympy_Rref\n```bash\nuv run python -m runtime.harness scripts\u002Fsympy_compute.py rref \"[[1,2,3],[4,5,6]]\"\n```\n\n### Z3_Prove\n```bash\nuv run python -m runtime.harness scripts\u002Fz3_solve.py prove \"subspace_closed\"\n```\n\n## Cognitive Tools Reference\n\nSee `.claude\u002Fskills\u002Fmath-mode\u002FSKILL.md` for full tool documentation.\n","# Vector Spaces\n\n## When to Use\n\nUse this skill when working on vector-spaces problems in linear algebra.\n\n## Decision Tree\n\n\n1. **Check Subspace**\n   - Contains zero vector?\n   - Closed under addition?\n   - Closed under scalar multiplication?\n   - Verify with `z3_solve.py prove`\n\n2. **Linear Independence**\n   - Set up Ax = 0 where columns are vectors\n   - `sympy_compute.py nullspace \"A\"`\n   - Trivial nullspace = independent\n\n3. **Basis and Dimension**\n   - Find spanning set, remove dependent vectors\n   - `sympy_compute.py rref \"A\"` to find pivot columns\n   - Dimension = number of pivots\n\n4. **Change of Basis**\n   - Find transition matrix P\n   - New coords = P^(-1) * old coords\n   - `sympy_compute.py inverse \"P\"`\n\n\n## Tool Commands\n\n### Sympy_Nullspace\n```bash\nuv run python -m runtime.harness scripts\u002Fsympy_compute.py nullspace \"[[1,2,3],[4,5,6]]\"\n```\n\n### Sympy_Rref\n```bash\nuv run python -m runtime.harness scripts\u002Fsympy_compute.py rref \"[[1,2,3],[4,5,6]]\"\n```\n\n### Z3_Prove\n```bash\nuv run python -m runtime.harness scripts\u002Fz3_solve.py prove \"subspace_closed\"\n```\n\n## Cognitive Tools Reference\n\nSee `.claude\u002Fskills\u002Fmath-mode\u002FSKILL.md` for full tool documentation.\n",{"name":5,"description":7,"allowed-tools":36},[23,37],"Read","main","70e1c350500ee750987420bbae48837afa906b7e","skills\u002Fmath\u002Flinear-algebra\u002Fvector-spaces","https:\u002F\u002Fgithub.com\u002Frubicanjr\u002FFinCognis","https:\u002F\u002Fgithub.com\u002Frubicanjr","linktr.ee\u002Ffinanskodu","Industrial Engineer & CIO @FinansKodu. Architecting AI-driven financial agents and autonomous workflows. 🏗️ Building systems, not just prompts.","2026-06-09 13:50:15",{"source":8,"skillName":5,"commands":47,"prompt":57,"zipAvailable":58},[48,51,54],{"tool":49,"command":50},"npx","npx skills add rubicanjr\u002FFinCognis --skill vector-spaces",{"tool":52,"command":53},"bunx","bunx skills add rubicanjr\u002FFinCognis --skill vector-spaces",{"tool":55,"command":56},"pnpm","pnpm dlx skills add rubicanjr\u002FFinCognis --skill vector-spaces","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002Frubicanjr\u002FFinCognis\u002Fblob\u002Fmain\u002Fskills\u002Fmath\u002Flinear-algebra\u002Fvector-spaces\u002FSKILL.md",true,[],[61,82,91,110,139,158],{"skillNo":62,"name":63,"nameZh":6,"description":64,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":65,"categories":66,"keywords":72,"publishedAt":31},"01M6NWS9DAXJTADT4T5MB49X8W","workflow-router","Goal-based workflow orchestration - routes tasks to specialist agents based on user goals","https:\u002F\u002Fgithub.com\u002Frubicanjr\u002FFinCognis\u002Fblob\u002Fmain\u002Fskills\u002Fworkflow-router\u002FSKILL.md",[67],{"categoryNo":68,"categoryName":69,"taxonomyType":70,"taxonomyTypeDesc":71},"01JBSEEDCAT000000000000023","Skill与智能体开发","SCENARIO","使用场景",[73,74,75,76,77,78,79,80,81],"workflow router","workflow","router","orchestration","goals","goal","user","workflow orchestration","tasks",{"skillNo":83,"name":84,"nameZh":6,"description":85,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":86,"categories":87,"keywords":88,"publishedAt":31},"01M6NWS3RETSC0SHP16HP66E14","wiring","Wiring Verification","https:\u002F\u002Fgithub.com\u002Frubicanjr\u002FFinCognis\u002Fblob\u002Fmain\u002Fskills\u002Fwiring\u002FSKILL.md",[],[84,89,90],"verification","false",{"skillNo":92,"name":93,"nameZh":6,"description":94,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":95,"categories":96,"keywords":100,"publishedAt":31},"01M6NWS0XW9CVQZBDA1EGW0TWC","websocket-patterns","Connection management, room patterns, reconnection strategies, message buffering, and binary protocol design.","https:\u002F\u002Fgithub.com\u002Frubicanjr\u002FFinCognis\u002Fblob\u002Fmain\u002Fskills\u002Fwebsocket-patterns\u002Fskill.md",[97],{"categoryNo":98,"categoryName":99,"taxonomyType":70,"taxonomyTypeDesc":71},"01JBSEEDCAT000000000000015","视觉设计",[101,102,103,104,105,106,107,26,108,109],"websocket","patterns","websocket patterns","design","protocol","management","message","binary","connection",{"skillNo":111,"name":112,"nameZh":6,"description":113,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":114,"categories":115,"keywords":120,"publishedAt":31},"01M6NWRDQDX9ZNETAWRRMQWV52","visual-verdict","Screenshot comparison QA for frontend development. 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