eigenvalues
Problem-solving strategies for eigenvalues in linear algebra
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- parcadei/Continuous-Claude-v3
- Last source activity
- January 10, 2026 at 01:54
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- eigenvalues
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- Problem-solving strategies for eigenvalues in linear algebra
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# 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
```bash
uv run python -m runtime.harness scripts/sympy_compute.py eigenvalues "[[1,2],[3,4]]"
```
### Sympy_Charpoly
```bash
uv run python -m runtime.harness scripts/sympy_compute.py charpoly "[[a,b],[c,d]]" --var lam
```
### Z3_Verify
```bash
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.
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