AgentSkillsCN

vector-spaces

线性代数向量空间问题的解题策略

SKILL.md
--- frontmatter
name: vector-spaces
description: "Problem-solving strategies for vector spaces in linear algebra"
allowed-tools: [Bash, Read]

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

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

Sympy_Rref

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

Z3_Prove

bash
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.