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vector-spaces

Problem-solving strategies for vector spaces in linear algebra

Stars
3,795
Source
parcadei/Continuous-Claude-v3
Updated
2026-01-26
Slug
parcadei--Continuous-Claude-v3--vector-spaces
View on GitHubRaw SKILL.md

// install — copy + paste into any project

mkdir -p .claude/skills && curl -fsSL https://raw.githubusercontent.com/parcadei/Continuous-Claude-v3/HEAD/.claude/skills/math/linear-algebra/vector-spaces/SKILL.md -o .claude/skills/vector-spaces.md

Drops the SKILL.md into .claude/skills/vector-spaces.md. Works with Claude Code, Cursor, and any agent that loads SKILL.md files from .claude/skills/.

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.