Vibecosystem vector-spaces

Problem-solving strategies for vector spaces in linear algebra

install

source · Clone the upstream repo

git clone https://github.com/vibeeval/vibecosystem

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/vibeeval/vibecosystem "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/math/linear-algebra/vector-spaces" ~/.claude/skills/vibeeval-vibecosystem-vector-spaces && rm -rf "$T"

manifest: skills/math/linear-algebra/vector-spaces/SKILL.md

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.