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  • Vector and Matrix Library User's Guide
    • Basic Concepts
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    • Structured Matrix Types
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  • Matrix Decompositions
    • 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

Matrix Decompositions

Extreme Optimization Numerical Libraries for .NET Professional

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.

The Extreme Optimization Numerical Libraries for .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

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