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EigenvalueDecompositionF Class

Determines the eigenvalues and eigenvectors of a real square matrix.
Inheritance Hierarchy
SystemObject
  Accord.Math.DecompositionsEigenvalueDecompositionF

Namespace:  Accord.Math.Decompositions
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.5.0
Syntax
public sealed class EigenvalueDecompositionF : ICloneable
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The EigenvalueDecompositionF type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyDiagonalMatrix
Returns the block diagonal eigenvalue matrix.
Public propertyEigenvectors
Returns the eigenvector matrix.
Public propertyImaginaryEigenvalues
Returns the imaginary parts of the eigenvalues.
Public propertyRank
Returns the effective numerical matrix rank.
Public propertyRealEigenvalues
Returns the real parts of the eigenvalues.
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodReverse
Reverses the decomposition, reconstructing the original matrix X.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by Matrix.)
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Remarks

In the mathematical discipline of linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.

If A is symmetric, then A = V * D * V' and A = V * V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. If A is not symmetric, the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A * V = V * D. The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V * D * inverse(V) depends upon the condition of V.

See Also