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Eigenvalues

Skill vibeeval/vibecosystem/skills/math/linear-algebra/eigenvalues

Problem-solving strategies for eigenvalues in linear algebraFrom its SKILL.md

Install
npx -y skills add vibeeval/vibecosystem --skill eigenvalues

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SKILL.md

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Eigenvalues

When to Use

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

Decision Tree

  1. Compute Characteristic Polynomial

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

  2. Find Eigenvalues

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

  3. Find Eigenvectors

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

  4. Verify

    • Check Av = lambda*v with z3_solve.py prove
    • Verify algebraic/geometric multiplicity

Tool Commands

Sympy_Eigenvalues

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

Sympy_Charpoly

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

Z3_Verify

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.

What ships with it

Read from the repository

Just SKILL.md. No reference files, no scripts.

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