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DigitalRuneEigenvalueDecompositionF Class
Computes the eigenvalues and eigenvectors of a real square matrix A (single-precision).
Inheritance Hierarchy
SystemObject
  DigitalRune.Mathematics.AlgebraEigenvalueDecompositionF

Namespace: DigitalRune.Mathematics.Algebra
Assembly: DigitalRune.Mathematics (in DigitalRune.Mathematics.dll) Version: 1.14.0.0 (1.14.0.14427)
Syntax
public class EigenvalueDecompositionF

The EigenvalueDecompositionF type exposes the following members.

Constructors
  NameDescription
Public methodEigenvalueDecompositionF
Creates the eigenvalue decomposition of the given matrix.
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Methods
  NameDescription
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Properties
  NameDescription
Public propertyD
Gets the block diagonal eigenvalue matrix D. (This property returns the internal matrix, not a copy.)
Public propertyImaginaryEigenvalues
Gets the vector of the imaginary parts of the eigenvalues.
Public propertyRealEigenvalues
Gets the vector of the real parts of the eigenvalues (the diagonal of D).
Public propertyV
Gets the eigenvector matrix V. (This property returns the internal matrix, not a copy.)
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Remarks

If the matrix A is symmetric, then A = V * D * VT where the eigenvalue matrix D is a diagonal matrix and the eigenvector matrix V is orthogonal.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1 x 1 blocks and any complex eigenvalues (λ + i*μ) in 2 x 2 blocks ((λ, μ),(-μ, λ)). 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 if the inverse of V can be computed depends on the condition number of V. (The condition number can be checked with SingularValueDecompositionF.)

See Also