CholeskyDecomposition Class

Represents the Cholesky decomposition of a positive-definite SymmetricMatrix.

For a list of all members of this type, see CholeskyDecomposition Members.

System.Object
   LinearTransformation
      Decomposition
         CholeskyDecomposition

[Visual Basic]
NotInheritable Public Class CholeskyDecomposition

Inherits Decomposition

[C#]

public sealed class CholeskyDecomposition : Decomposition

Remarks

The Cholesky decomposition of a real symmetric positive definite matrix A rewrites the matrix in the form A= LL^T, where L is a lower-triangular matrix.

CholeskyDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten with the result of the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

CholeskyDecomposition inherits from LinearTransformation. This means you can use it to solve systems of linear equations where the matrix of the system is symmetric and positive definite. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve method. You can also calculate the determinant the inverse, and an estimate for the condition number.

To solve a general (non-symmetric or non-positive definite)system of equations, use the LUDecomposition class instead.

Requirements

Namespace: Extreme.Mathematics.LinearAlgebra

Assembly: Extreme.Mathematics (in Extreme.Mathematics.dll)

CholeskyDecomposition Class

Remarks

Requirements

See Also