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/vector-spaces

Problem-solving strategies for vector spaces in linear algebra

From plugin
vibecosystem
547200 skills138 agents7 hooks

Claude Code

$ npx -y skills add vibeeval/vibecosystem --skill vector-spaces --agent claude-code

SKILL.md

vector-spaces.SKILL.md
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

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

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.

@vibeeval
Ships withvibecosystem

A focused runtime for Claude Code. A bounded worker for Codex. Catalog (in repo): Default core: vibecosystem packages agents, skills and hooks for software work.

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Questions about vector-spaces.

Which coding agents can use vector-spaces?
vector-spaces installs in Claude Code, Codex, Cursor, Gemini CLI, GitHub Copilot, OpenCode and Windsurf with the skills CLI, using each agent's flag shown on this page. Flowy's auto-invocation, which fires a skill when your prompt matches, runs in Claude Code only.