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Vector Spaces — measured AI agent skill | DecimalAI

vibeeval/vector-spaces

SkillScore91Maintained

Problem-solving strategies for vector spaces in linear algebra

by vibeeval

Links this skill to your agents and keeps it current with the author’s updates.

Automatic

Tutoring & Education pack

decimalai skills pull vibeeval-vector-spaces

Get this skill — curl · raw file

curl -fsSL https://app.decimal.ai/s/vibeeval-vector-spaces/SKILL.md

Raw file: /s/vibeeval-vector-spaces/SKILL.md ↗ · machine-readable summary at /s/vibeeval-vector-spaces.json ↗

In productionGlobal

how this skill behaves on real traffic · last 30 days

No production data for this skill yet — usage numbers appear here once agents start running it.

Anonymized aggregate across every org using this skill — proof from real production use, not a demo.

Does this skill help? · Benchmark: with vs. withoutsign in to run this on your agents

23 test cases from the publisher’s eval.yaml · each run twice on gemini-3.6-flash — with the skill injected, then without · last run 6d ago

Yes — +17% lift-5% tokens0% turns91% of whole cases pass with skill (21/23)

Test case	Without → With	Effect	Δ tokens	Δ turns
case-02	✗→✓	▲ Improved	-56%	0%
case-04	✗→✓	▲ Improved	-52%	0%
case-06	✗→✓	▲ Improved	-43%	0%
case-10	✗→✓	▲ Improved	-40%	0%
case-14	✗→✓	▲ Improved	-56%	0%

Showing 5 of 23 cases

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

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

View on GitHub ↗

License MITImported 8/1/2026Version v1

Skill contents

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

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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Other measured skills in the registry, with their headline benchmark lift.