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Eigenvalues — measured AI agent skill | DecimalAI

vibeeval/eigenvalues

SkillScore32Maintained

Problem-solving strategies for eigenvalues 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-eigenvalues

Get this skill — curl · raw file

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

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

22 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

—-8% tokens0% turns32% of whole cases pass with skill (7/22)

Test case	Without → With	Effect	Δ tokens	Δ turns
case-11	✗→✓	▲ Improved	-58%	0%
case-13	✗→✓	▲ Improved	-49%	0%
case-12	✓→✓	＝ Same ✓	-22%	0%
case-14	✓→✓	＝ Same ✓	9%	0%
case-20	✓→✓	＝ Same ✓	2%	0%

Showing 5 of 22 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/eigenvalues/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

Skill contents

SKILL.md

Eigenvalues

When to Use

Use this skill when working on eigenvalues problems in linear algebra.

Decision Tree

Compute Characteristic Polynomial

det(A - lambdaI) = 0
sympy_compute.py charpoly "[[a,b],[c,d]]" --var lam

Find Eigenvalues

Solve characteristic polynomial
sympy_compute.py eigenvalues "[[1,2],[3,4]]"

Find Eigenvectors

For each eigenvalue lambda: solve (A - lambdaI)v = 0
sympy_compute.py eigenvectors "[[1,2],[3,4]]"

Verify

Check Av = lambdav with z3_solve.py prove
Verify algebraic/geometric multiplicity

Tool Commands

Sympy_Eigenvalues

bash
uv run python -m runtime.harness scripts/sympy_compute.py eigenvalues "[[1,2],[3,4]]"

Sympy_Charpoly

bash
uv run python -m runtime.harness scripts/sympy_compute.py charpoly "[[a,b],[c,d]]" --var lam

Z3_Verify

bash
uv run python -m runtime.harness scripts/z3_solve.py sat "det(A - lambda*I) == 0"

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

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