/eigenvalues

name: eigenvalues
description: "Problem-solving strategies for eigenvalues in linear algebra"
allowed-tools: [Bash, Read]

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.