> ## Documentation Index
> Fetch the complete documentation index at: https://math.aboneda.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Introduction to Algebra

> Foundations of abstract and linear algebra

# Algebra

Algebra studies mathematical structures such as groups, rings, fields, and vector spaces. It generalizes arithmetic and provides the language for modern mathematics.

## Key Topics

* **Linear Algebra** — vectors, matrices, linear transformations, eigenvalues
* **Group Theory** — groups, subgroups, homomorphisms, symmetry
* **Ring Theory** — rings, ideals, polynomial rings
* **Field Theory** — fields, extensions, Galois theory
* **Vector Spaces** — bases, dimension, inner product spaces
* **Matrix Decompositions** — LU, QR, SVD, eigendecomposition
* **Systems of Equations** — Gaussian elimination, rank, nullity
* **Abstract Algebra Applications** — coding theory, cryptography