Vibecosystem eigenvalues

Problem-solving strategies for eigenvalues in linear algebra

install

source · Clone the upstream repo

git clone https://github.com/vibeeval/vibecosystem

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/vibeeval/vibecosystem "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/math/linear-algebra/eigenvalues" ~/.claude/skills/vibeeval-vibecosystem-eigenvalues && rm -rf "$T"

manifest: skills/math/linear-algebra/eigenvalues/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.