EigenDecomposition ("The Adobe AEM Quickstart and Web Application.")

All Known Implementing Classes:

EigenDecompositionImpl
```
public interface EigenDecomposition
```
An interface to classes that implement an algorithm to calculate the eigen decomposition of a real matrix.
The eigen decomposition of matrix A is a set of two matrices: V and D such that A = V × D × V^T. A, V and D are all m × m matrices.

This interface is similar in spirit to the EigenvalueDecomposition class from the JAMA library, with the following changes:
- a getVt method has been added,
- two getRealEigenvalue and getImagEigenvalue methods to pick up a single eigenvalue have been added,
- a getEigenvector method to pick up a single eigenvector has been added,
- a getDeterminant method has been added.
- a getSolver method has been added.
Since:

2.0

See Also:

MathWorld, Wikipedia

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method and Description
`RealMatrix`	`getD()` Returns the block diagonal matrix D of the decomposition.
`double`	`getDeterminant()` Return the determinant of the matrix
`RealVector`	`getEigenvector(int i)` Returns a copy of the i^th eigenvector of the original matrix.
`double`	`getImagEigenvalue(int i)` Returns the imaginary part of the i^th eigenvalue of the original matrix.
`double[]`	`getImagEigenvalues()` Returns a copy of the imaginary parts of the eigenvalues of the original matrix.
`double`	`getRealEigenvalue(int i)` Returns the real part of the i^th eigenvalue of the original matrix.
`double[]`	`getRealEigenvalues()` Returns a copy of the real parts of the eigenvalues of the original matrix.
`DecompositionSolver`	`getSolver()` Get a solver for finding the A × X = B solution in exact linear sense.
`RealMatrix`	`getV()` Returns the matrix V of the decomposition.
`RealMatrix`	`getVT()` Returns the transpose of the matrix V of the decomposition.

- Method Detail
  - getV
```
RealMatrix getV()
```
    Returns the matrix V of the decomposition.
    V is an orthogonal matrix, i.e. its transpose is also its inverse.
    
    The columns of V are the eigenvectors of the original matrix.
    
    No assumption is made about the orientation of the system axes formed by the columns of V (e.g. in a 3-dimension space, V can form a left- or right-handed system).
    
    Returns:
    
    the V matrix
  - getD
```
RealMatrix getD()
```
    Returns the block diagonal matrix D of the decomposition.
    D is a block diagonal matrix.
    
    Real eigenvalues are on the diagonal while complex values are on 2x2 blocks { {real +imaginary}, {-imaginary, real} }.
    
    Returns:
    
    the D matrix
    
    See Also:
    
    getRealEigenvalues(), getImagEigenvalues()
  - getVT
```
RealMatrix getVT()
```
    Returns the transpose of the matrix V of the decomposition.
    V is an orthogonal matrix, i.e. its transpose is also its inverse.
    
    The columns of V are the eigenvectors of the original matrix.
    
    No assumption is made about the orientation of the system axes formed by the columns of V (e.g. in a 3-dimension space, V can form a left- or right-handed system).
    
    Returns:
    
    the transpose of the V matrix
  - getRealEigenvalues
```
double[] getRealEigenvalues()
```
    Returns a copy of the real parts of the eigenvalues of the original matrix.
    
    Returns:
    
    a copy of the real parts of the eigenvalues of the original matrix
    
    See Also:
    
    getD(), getRealEigenvalue(int), getImagEigenvalues()
  - getRealEigenvalue
```
double getRealEigenvalue(int i)
```
    Returns the real part of the i^th eigenvalue of the original matrix.
    
    Parameters:
    
    i - index of the eigenvalue (counting from 0)
    
    Returns:
    
    real part of the i^th eigenvalue of the original matrix
    
    See Also:
    
    getD(), getRealEigenvalues(), getImagEigenvalue(int)
  - getImagEigenvalues
```
double[] getImagEigenvalues()
```
    Returns a copy of the imaginary parts of the eigenvalues of the original matrix.
    
    Returns:
    
    a copy of the imaginary parts of the eigenvalues of the original matrix
    
    See Also:
    
    getD(), getImagEigenvalue(int), getRealEigenvalues()
  - getImagEigenvalue
```
double getImagEigenvalue(int i)
```
    Returns the imaginary part of the i^th eigenvalue of the original matrix.
    
    Parameters:
    
    i - index of the eigenvalue (counting from 0)
    
    Returns:
    
    imaginary part of the i^th eigenvalue of the original matrix
    
    See Also:
    
    getD(), getImagEigenvalues(), getRealEigenvalue(int)
  - getEigenvector
```
RealVector getEigenvector(int i)
```
    Returns a copy of the i^th eigenvector of the original matrix.
    
    Parameters:
    
    i - index of the eigenvector (counting from 0)
    
    Returns:
    
    copy of the i^th eigenvector of the original matrix
    
    See Also:
    
    getD()
  - getDeterminant
```
double getDeterminant()
```
    Return the determinant of the matrix
    
    Returns:
    
    determinant of the matrix
  - getSolver
```
DecompositionSolver getSolver()
```
    Get a solver for finding the A × X = B solution in exact linear sense.
    
    Returns:
    
    a solver

Interface EigenDecomposition

Method Summary

Method Detail

getV

getD

getVT

getRealEigenvalues

getRealEigenvalue

getImagEigenvalues

getImagEigenvalue

getEigenvector

getDeterminant

getSolver