vector-spaces
Automated problem-solving for vector spaces using SymPy and Z3 solvers for linear algebra tasks.
Install
mkdir -p .claude/skills/vector-spaces && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/2006" && unzip -o skill.zip -d .claude/skills/vector-spaces && rm skill.zipInstalls to .claude/skills/vector-spaces
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for vector spaces in linear algebraKey capabilities
- →Verifies subspace properties using Z3
- →Computes nullspaces to determine linear independence
- →Calculates basis and dimension using RREF
- →Computes inverse matrices for change of basis
How it works
The skill follows a decision tree to apply specific Python scripts for subspace verification, nullspace computation, and matrix reduction. It utilizes Z3 and SymPy for mathematical proofs and calculations.
Inputs & outputs
When to use vector-spaces
- →Check if a set forms a subspace
- →Determine linear independence of vectors
- →Calculate the basis and dimension of a span
- →Find change of basis matrices
About this skill
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.
When not to use it
- →When solving problems outside of linear algebra vector spaces
Limitations
- →Requires input matrices to be formatted as nested lists for script compatibility
How it compares
It provides a structured decision tree and automated command-line execution for linear algebra operations instead of manual calculation.
Compared to similar skills
vector-spaces side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| vector-spaces (this skill) | 2 | 7mo | Review | Intermediate |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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