eigenvalues

Eigenvalues

When to Use

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

Decision Tree

1. Compute Characteristic Polynomial
2. det(A - lambda*I) = 0
3. sympy_compute.py charpoly "[[a,b],[c,d]]" --var lam

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

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

1. Verify
2. Check Av = lambda*v with z3_solve.py prove
3. 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.