EigenvalueDecompositionF Class |
Namespace: DigitalRune.Mathematics.Algebra
The EigenvalueDecompositionF type exposes the following members.
Name | Description | |
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EigenvalueDecompositionF |
Creates the eigenvalue decomposition of the given matrix.
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Name | Description | |
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Equals | (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it 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.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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D |
Gets the block diagonal eigenvalue matrix D. (This property returns the internal matrix,
not a copy.)
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ImaginaryEigenvalues |
Gets the vector of the imaginary parts of the eigenvalues.
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RealEigenvalues |
Gets the vector of the real parts of the eigenvalues (the diagonal of D).
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V |
Gets the eigenvector matrix V. (This property returns the internal matrix,
not a copy.)
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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.)