# Matrix Decompositions

A matrix decomposition or factorization is a representation of a matrix as a product of two or more
matrices. Decomposing a matrix is often the first step in the solution of a problem in linear algebra. The
matrices in the decomposition usually have some special properties, which can be used to simplify the solution. A
decomposition is often called a *factorization*. The two words are synonyms.

**Extreme Numerics.NET** contains a series of classes that implement a
number of standard decompositions. These classes are contained in the Extreme.Mathematics.LinearAlgebra namespace.

In this section:

- The LU Decomposition
- The QR Decomposition
- The Cholesky Decomposition
- The Symmetric Indefinite Decomposition
- The Eigenvalue Decomposition
- The Generalized Eigenvalue Decomposition
- The Singular Value Decomposition
- The Generalized Singular Value Decomposition
- Non-Negative Matrix Factorization
- Solving Linear Systems