Eigenvalues

When to Use

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