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Vector Spaces

vibeeval/vector-spaces

Problem-solving strategies for vector spaces in linear algebra

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521
stars on the repo
on the repository, not the skill itself

Install

one command, takes just this skill from the repository 
npx skills add https://github.com/vibeeval/vibecosystem --skill vector-spaces

The instruction itself

8 sections, as written by the author

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.

How to use it

Copy the folder

Take vibeeval/vector-spaces from the repository into ~/.claude/skills for personal use, or into .claude/skills inside a project.

Check the name does not clash

The agent identifies a skill by the name field in its header. Two skills with the same name cannot sit side by side — one of them will be ignored.