vector-spaces
Problem-solving strategies for vector spaces in linear algebra
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技能内容
Vector Spaces
When to Use
Use this skill when working on vector-spaces problems in linear algebra.
Decision Tree
- Check Subspace
- Contains zero vector?
- Closed under addition?
- Closed under scalar multiplication?
- Verify with
z3_solve.py prove
- Linear Independence
- Set up Ax = 0 where columns are vectors
sympy_compute.py nullspace "A"- Trivial nullspace = independent
- Basis and Dimension
- Find spanning set, remove dependent vectors
sympy_compute.py rref "A"to find pivot columns- Dimension = number of pivots
- 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.
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原文件路径
.claude/skills/math/linear-algebra/vector-spaces/SKILL.md