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<h2 class="chapter">14 Eigensystems</h2>
<p><a name="index-eigenvalues-and-eigenvectors-1330"></a>This chapter describes functions for computing eigenvalues and
eigenvectors of matrices. There are routines for real symmetric,
real nonsymmetric, complex hermitian, real generalized symmetric-definite,
complex generalized hermitian-definite, and real generalized nonsymmetric
eigensystems. Eigenvalues can be computed with or without eigenvectors.
The hermitian and real symmetric matrix algorithms are symmetric bidiagonalization
followed by QR reduction. The nonsymmetric algorithm is the Francis QR
double-shift. The generalized nonsymmetric algorithm is the QZ method due
to Moler and Stewart.
<p>The functions described in this chapter are declared in the header file
<samp><span class="file">gsl_eigen.h</span></samp>.
<ul class="menu">
<li><a accesskey="1" href="Real-Symmetric-Matrices.html">Real Symmetric Matrices</a>
<li><a accesskey="2" href="Complex-Hermitian-Matrices.html">Complex Hermitian Matrices</a>
<li><a accesskey="3" href="Real-Nonsymmetric-Matrices.html">Real Nonsymmetric Matrices</a>
<li><a accesskey="4" href="Real-Generalized-Symmetric_002dDefinite-Eigensystems.html">Real Generalized Symmetric-Definite Eigensystems</a>
<li><a accesskey="5" href="Complex-Generalized-Hermitian_002dDefinite-Eigensystems.html">Complex Generalized Hermitian-Definite Eigensystems</a>
<li><a accesskey="6" href="Real-Generalized-Nonsymmetric-Eigensystems.html">Real Generalized Nonsymmetric Eigensystems</a>
<li><a accesskey="7" href="Sorting-Eigenvalues-and-Eigenvectors.html">Sorting Eigenvalues and Eigenvectors</a>
<li><a accesskey="8" href="Eigenvalue-and-Eigenvector-Examples.html">Eigenvalue and Eigenvector Examples</a>
<li><a accesskey="9" href="Eigenvalue-and-Eigenvector-References.html">Eigenvalue and Eigenvector References</a>
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