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