SKILL.md
Eigenvalues
When to Use
Use this skill when working on eigenvalues problems in linear algebra.
Decision Tree
- Compute Characteristic Polynomial
- det(A - lambda*I) = 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 - lambda*I)v = 0 - sympy_compute.py eigenvectors "[[1,2],[3,4]]"
- 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.