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eigenvalues

Problem-solving strategies for eigenvalues in linear algebra

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SKILL.md

Full skill instructions

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.