﻿ JaggedEigenvalueDecomposition Class   # JaggedEigenvalueDecomposition Class

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

Namespace:  Accord.Math.Decompositions
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0 Syntax
`public sealed class JaggedEigenvalueDecomposition : ICloneable`

The JaggedEigenvalueDecomposition type exposes the following members. Constructors
NameDescription JaggedEigenvalueDecomposition(Double, Boolean, Boolean)
Construct an eigenvalue decomposition. JaggedEigenvalueDecomposition(Double, Boolean, Boolean, Boolean)
Construct an eigenvalue decomposition.
Top Properties
NameDescription DiagonalMatrix
Returns the block diagonal eigenvalue matrix. Eigenvectors
Returns the eigenvector matrix. ImaginaryEigenvalues
Returns the imaginary parts of the eigenvalues. Rank
Returns the effective numerical matrix rank. RealEigenvalues
Returns the real parts of the eigenvalues.
Top Methods
NameDescription Clone
Creates a new object that is a copy of the current instance. Equals
Determines whether the specified object is equal to the current object.
(Inherited from Object.) GetHashCode
Serves as the default hash function.
(Inherited from Object.) GetType
Gets the Type of the current instance.
(Inherited from Object.) Reverse
Reverses the decomposition, reconstructing the original matrix X. ToString
Returns a string that represents the current object.
(Inherited from Object.)
Top Extension Methods
NameDescription HasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.) IsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.) To(Type)Overloaded.
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.) ToTOverloaded.
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.)
Top 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