vector-spaces

Problem-solving strategies for vector spaces in linear algebra

422 stars

Best use case

vector-spaces is best used when you need a repeatable AI agent workflow instead of a one-off prompt.

Problem-solving strategies for vector spaces in linear algebra

Teams using vector-spaces should expect a more consistent output, faster repeated execution, less prompt rewriting.

When to use this skill

  • You want a reusable workflow that can be run more than once with consistent structure.

When not to use this skill

  • You only need a quick one-off answer and do not need a reusable workflow.
  • You cannot install or maintain the underlying files, dependencies, or repository context.

Installation

Claude Code / Cursor / Codex

$curl -o ~/.claude/skills/vector-spaces/SKILL.md --create-dirs "https://raw.githubusercontent.com/vibeeval/vibecosystem/main/skills/math/linear-algebra/vector-spaces/SKILL.md"

Manual Installation

  1. Download SKILL.md from GitHub
  2. Place it in .claude/skills/vector-spaces/SKILL.md inside your project
  3. Restart your AI agent — it will auto-discover the skill

How vector-spaces Compares

Feature / Agentvector-spacesStandard Approach
Platform SupportNot specifiedLimited / Varies
Context Awareness High Baseline
Installation ComplexityUnknownN/A

Frequently Asked Questions

What does this skill do?

Problem-solving strategies for vector spaces in linear algebra

Where can I find the source code?

You can find the source code on GitHub using the link provided at the top of the page.

SKILL.md Source

# Vector Spaces

## When to Use

Use this skill when working on vector-spaces problems in linear algebra.

## Decision Tree


1. **Check Subspace**
   - Contains zero vector?
   - Closed under addition?
   - Closed under scalar multiplication?
   - Verify with `z3_solve.py prove`

2. **Linear Independence**
   - Set up Ax = 0 where columns are vectors
   - `sympy_compute.py nullspace "A"`
   - Trivial nullspace = independent

3. **Basis and Dimension**
   - Find spanning set, remove dependent vectors
   - `sympy_compute.py rref "A"` to find pivot columns
   - Dimension = number of pivots

4. **Change of Basis**
   - Find transition matrix P
   - New coords = P^(-1) * old coords
   - `sympy_compute.py inverse "P"`


## Tool Commands

### Sympy_Nullspace
```bash
uv run python -m runtime.harness scripts/sympy_compute.py nullspace "[[1,2,3],[4,5,6]]"
```

### Sympy_Rref
```bash
uv run python -m runtime.harness scripts/sympy_compute.py rref "[[1,2,3],[4,5,6]]"
```

### Z3_Prove
```bash
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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