# Algebra

> Solves equations, factors expressions, and analyzes algebraic structures including matrices, vector spaces, and group theory.

- Skill: `neuralblitz/algebra` (Agent Skill)
- Install (CLI): `npx skillmds@latest add neuralblitz/algebra`
- Raw SKILL.md: https://api.skillmd.com/api/skills/neuralblitz/algebra/raw
- Safety review: PASS (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Tags: Algebra, Equations, Group Theory, Linear Algebra, Mathematics, Matrices
- License: MIT
- Author: NeuralBlitz (https://skillmd.com/u/neuralblitz)
- Updated: 2026-08-22
- Page: https://skillmd.com/skills/neuralblitz/algebra

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## What I do
- Solve equations and polynomial roots
- Factor expressions and find greatest common divisors
- Work with matrices and linear transformations
- Apply group, ring, and field theory
- Analyze vector spaces and basis transformations
- Solve systems of linear equations

## When to use me
When solving mathematical problems, working with abstract algebraic structures, or optimizing linear systems.

## Key Concepts
- **Quadratic Formula**: x = (-b ± √(b²-4ac))/2a for ax² + bx + c = 0
- **Matrix Multiplication**: (AB)_{ij} = Σ_k A_{ik}B_{kj}
- **Determinant**: det(A) nonzero implies matrix invertible
- **Eigenvalues**: Solutions to det(A - λI) = 0
- **Group**: Set with associative binary operation, identity, inverses
- **Field**: Commutative ring where nonzero elements form group