org.apache.commons.math.linear

## Interface EigenDecomposition

• ### Method Summary

All 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 ith eigenvector of the original matrix.
`double` `getImagEigenvalue(int i)`
Returns the imaginary part of the ith 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 ith 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
`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
• #### getEigenvector

`RealVector getEigenvector(int i)`
Returns a copy of the ith eigenvector of the original matrix.
Parameters:
`i` - index of the eigenvector (counting from 0)
Returns:
copy of the ith eigenvector of the original matrix
`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