thedixitjain 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.
Source: parcadei/Continuous-Claude-v3 → .claude/skills/math/linear-algebra/vector-spaces/SKILL.md