# Interface EigenDecomposition<T extends Matrix>

All Superinterfaces:
`DecompositionInterface<T>`
All Known Subinterfaces:
`EigenDecomposition_F32<MatrixType>`, `EigenDecomposition_F64<MatrixType>`
All Known Implementing Classes:
`SwitchingEigenDecomposition_DDRM`, `SwitchingEigenDecomposition_FDRM`, `SymmetricQRAlgorithmDecomposition_DDRM`, `SymmetricQRAlgorithmDecomposition_FDRM`, `WatchedDoubleStepQRDecomposition_DDRM`, `WatchedDoubleStepQRDecomposition_FDRM`

```public interface EigenDecomposition<T extends Matrix>
extends DecompositionInterface<T>```

This is a generic interface for computing the eigenvalues and eigenvectors of a matrix. Eigenvalues and eigenvectors have the following property:

A*v=λ*v

where A is a square matrix and v is an eigenvector associated with the eigenvalue λ.

In general, both eigenvalues and eigenvectors can be complex numbers. For symmetric matrices the eigenvalues and eigenvectors are always real numbers. EJML does not support complex matrices but it does have minimal support for complex numbers. As a result complex eigenvalues are found, but only the real eigenvectors are computed.

To create a new instance of `EigenDecomposition` use DecompositionFactory_XXXX. If the matrix is known to be symmetric be sure to use the symmetric decomposition, which is much faster and more accurate than the general purpose one.

• ## Method Summary

Modifier and Type Method Description
`T` `getEigenVector​(int index)`
Used to retrieve real valued eigenvectors.
`int` `getNumberOfEigenvalues()`
Returns the number of eigenvalues/eigenvectors.

### Methods inherited from interface org.ejml.interfaces.decomposition.DecompositionInterface

`decompose, inputModified`
• ## Method Details

• ### getNumberOfEigenvalues

int getNumberOfEigenvalues()
Returns the number of eigenvalues/eigenvectors. This is the matrix's dimension.
Returns:
number of eigenvalues/eigenvectors.
• ### getEigenVector

T getEigenVector​(int index)

Used to retrieve real valued eigenvectors. If an eigenvector is associated with a complex eigenvalue then null is returned instead.

Parameters:
`index` - Index of the eigenvalue eigenvector pair.
Returns:
If the associated eigenvalue is real then an eigenvector is returned, null otherwise.