﻿CholeskyDecomposition Class
Represents the Cholesky Decomposition of a symmetric, positive definite matrix.

Namespace: Meta.Numerics.Matrices
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.1.0.0 (2.1.0.0)

# Syntax

 C# Visual Basic Visual C++ F#
`public sealed class CholeskyDecomposition`
`Public NotInheritable Class CholeskyDecomposition`
`public ref class CholeskyDecomposition sealed`
```[<SealedAttribute>]
type CholeskyDecomposition =  class end```

# Members

 All Members Properties Methods
 Public Protected Instance Static Declared Inherited XNA Framework Only  .NET Compact Framework Only
MemberDescription
Determinant()()()()
Computes the determinant of the original matrix.
Dimension
Gets the dimension of the system.
Equals(Object)
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Finalize()()()()
Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
(Inherited from Object.)
GetHashCode()()()()
Serves as a hash function for a particular type.
(Inherited from Object.)
GetType()()()()
Gets the Type of the current instance.
(Inherited from Object.)
Inverse()()()()
Computes the inverse of the original matrix.
MemberwiseClone()()()()
Creates a shallow copy of the current Object.
(Inherited from Object.)
Solve(IList<(Of <<'(Double>)>>))
Computes the solution vector that, when multiplied by the original matrix, produces the given left-hand side vector.
SquareRootMatrix()()()()
Returns the Cholesky square root matrix.
ToString()()()()
Returns a String that represents the current Object.
(Inherited from Object.)

# Remarks

A Cholesky decomposition represents a matrix as the product of a lower-left triangular matrix and its transpose. For example:

The Choleksy decomposition of a symmetric, positive definite matrix can be obtained using the CholeskyDecomposition()()()() method of the SymmetricMatrix class.

# Examples

Here is an example that uses a Cholesky decomposition to solve a linear algebra problem.

CopyC#
```// Solve Ax = b via Cholesky decomposition
CholeskyDecomposition CD = A.CholsekyDecomposition();
ColumnVector b = new ColumnVector(1.0, 2.0, 3.0);
ColumnVector x CD.Solve(b);```

# Inheritance Hierarchy

System..::..Object
Meta.Numerics.Matrices..::..CholeskyDecomposition