**Chapter
23. **** EigenValue Problems** (.NET, C#, CSharp, VB, Visual Basic, F#)

**NMath** includes
classes for solving symmetric, Hermitian, and nonsymmetric eigenvalue
problems. The classical eigenvalue problem is defined as the solution
to:

for a matrix , eigenvectors ,
and the diagonal matrix of eigenvalues . **NMath**
also provides eigenvalue *server*
classes that construct instances of the eigenvalue classes, allowing
you greater control over how the eigenvalue decomposition is performed.

For example, class **DoubleSymEigDecomp**
computes the eigenvalues and eigenvectors of a **DoubleSymmetricMatrix**.
By default, this class computes both eigenvalues and eigenvectors. For
more control, the associated decomposition server class, **DoubleSymEigDecompServer**, can be configured
to compute eigenvalues only, or both eigenvalues and eigenvectors. In
addition, the server can be configured to compute only the eigenvalues
in a given range. A tolerance for the convergence of the algorithm may
also be specified.

This chapter describes the **NMath**
eigenvalue and eigenvalue server classes, and how to construct and use
them.