com.numericalmethod.suanshu.matrix.doubles.factorization.eigen
Interface EigenDecomposition

All Known Implementing Classes:

Eigen

public interface EigenDecomposition

Let A be a square (N×N) matrix with N linearly independent eigenvectors. Then A can be factorized as

 Q %*% D %*% Q' = A
 

where Q is the square (N×N) matrix whose i-th column is the eigenvector of A, and D is the diagonal matrix whose diagonal elements are the corresponding eigenvalues.

Note that only diagonalizable matrices can be factorized in this way.

See Also:

Wikipedia: Eigendecomposition of a matrix

Method Summary

DiagonalMatrix	D() Get a copy of the diagonal matrix D as in Q %*% D %*% Q' = A Note that we only support real eigenvalues for now.
Matrix	Q() Get a copy of Q as in Q %*% D %*% Q' = A Note that we only support real eigenvalues for now.
Matrix	Qt() Get a copy of Q.t() as in Q %*% D %*% Q' = A Note that we only support real eigenvalues for now.

Method Detail

D

DiagonalMatrix D()

Get a copy of the diagonal matrix D as in

 Q %*% D %*% Q' = A
 

Note that we only support real eigenvalues for now.

Returns:

a copy of D

Q

Matrix Q()

Get a copy of Q as in

 Q %*% D %*% Q' = A
 

Note that we only support real eigenvalues for now.

Returns:

a copy of Q

Qt

Matrix Qt()

Get a copy of Q.t() as in

 Q %*% D %*% Q' = A
 

Note that we only support real eigenvalues for now.

Returns:

a copy of Q.t()