Represents the symmetric eigenvalue decomposition of a SymmetricMatrix.

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (Extreme.Numerics)

Syntax

Visual Basic (Declaration)
Public Class SymmetricEigenvalueDecomposition _
	Inherits Decomposition
C#
public class SymmetricEigenvalueDecomposition : Decomposition
C++
public ref class SymmetricEigenvalueDecomposition : public Decomposition

Methods

IconTypeDescription
Decompose()
Calculates the actual eigenvalue decomposition.
Equals(Object)
Determines whether the specified Object is equal to the current Object.
EstimateConditionNumber()
Calculates an estimate for the condition number of the Matrix.
Finalize()
Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
GetDeterminant()
Calculates the determinant of the decomposed Matrix.
GetHashCode()
Serves as a hash function for a particular type.
GetInverse()
Calculates the inverse of the factorized Matrix.
GetObjectData(SerializationInfo, StreamingContext)
Populates a SerializationInfo with the data needed to serialize the target object.
GetType()
Gets the Type of the current instance.
IsSingular()
Gets a value indicating whether the BaseMatrix of this decomposition is singular.
MemberwiseClone()
Creates a shallow copy of the current Object.
Rank(Double)
Returns the numerical rank of a matrix using the specified tolerance.
SetSingularFlag()
Sets a flag that indicates the underlying matrix of this decomposition is singular.
Solve(GeneralMatrix, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side GeneralMatrix and overwrites the right-hand side with the solution.
Solve(GeneralVector, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side Vector.
Solve(Vector)
Solves the system of linear equations for the specified right-hand side Vector.
Solve(Matrix)
Solves the system of linear equations for the specified right-hand side Matrix.
ToString()
Returns a String that represents the current Object.

Constructors

IconTypeDescription
SymmetricEigenvalueDecompositionNew(SymmetricMatrix)
Constructs a new SymmetricEigenvalueDecomposition object.
SymmetricEigenvalueDecompositionNew(SymmetricMatrix, Boolean)
Constructs a new SymmetricEigenvalueDecomposition object.

Properties

IconTypeDescription
BaseMatrix
Gets the underlying matrix of the decomposition.
Done
Gets or sets a value that indicates whether the decomposition has been performed.
Eigenvalues
Gets the eigenvalues of the matrix.
Eigenvectors
Gets the eigenvectors of the matrix.
Overwrite
Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.

Remarks

The symmetric eigenvalue decomposition of a real symmetric matrix A rewrites the matrix in the form A= XLX-1, where X is an orthogonal matrix and L is a diagonal matrix.

SymmetricEigenvalueDecomposition 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.

SymmetricEigenvalueDecomposition 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(GeneralMatrix, Boolean) method. You can also calculate the GetDeterminant() the GetInverse(), and an estimate for the EstimateConditionNumber().

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

Inheritance Hierarchy

System.Object
  Extreme.Mathematics.LinearAlgebra.LinearTransformation
    Extreme.Mathematics.LinearAlgebra.Decomposition
      Extreme.Mathematics.LinearAlgebra.SymmetricEigenvalueDecomposition

See Also