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Vector spaces

Skill parcadei/Continuous-Claude-v3/.claude/skills/math/linear-algebra/vector-spaces

Problem-solving strategies for vector spaces in linear algebraFrom its SKILL.md

Install
npx -y skills add parcadei/Continuous-Claude-v3 --skill vector-spaces

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SKILL.md

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Vector Spaces

When to Use

Use this skill when working on vector-spaces problems in linear algebra.

Decision Tree

  1. Check Subspace

    • Contains zero vector?
    • Closed under addition?
    • Closed under scalar multiplication?
    • Verify with z3_solve.py prove

  2. Linear Independence

    • Set up Ax = 0 where columns are vectors
    • sympy_compute.py nullspace "A"
    • Trivial nullspace = independent

  3. Basis and Dimension

    • Find spanning set, remove dependent vectors
    • sympy_compute.py rref "A" to find pivot columns
    • Dimension = number of pivots

  4. Change of Basis

    • Find transition matrix P
    • New coords = P^(-1) * old coords
    • sympy_compute.py inverse "P"

Tool Commands

Sympy_Nullspace

uv run python -m runtime.harness scripts/sympy_compute.py nullspace "[[1,2,3],[4,5,6]]"

Sympy_Rref

uv run python -m runtime.harness scripts/sympy_compute.py rref "[[1,2,3],[4,5,6]]"

Z3_Prove

uv run python -m runtime.harness scripts/z3_solve.py prove "subspace_closed"

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

What ships with it

Read from the repository

Just SKILL.md. No reference files, no scripts.

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