| 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
-
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.