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<h3 class="section">13.6 Tridiagonal Decomposition of Real Symmetric Matrices</h3>
<p><a name="index-tridiagonal-decomposition-1288"></a>
A symmetric matrix A can be factorized by similarity
transformations into the form,
<pre class="example"> A = Q T Q^T
</pre>
<p class="noindent">where Q is an orthogonal matrix and T is a symmetric
tridiagonal matrix.
<div class="defun">
— Function: int <b>gsl_linalg_symmtd_decomp</b> (<var>gsl_matrix * A, gsl_vector * tau</var>)<var><a name="index-gsl_005flinalg_005fsymmtd_005fdecomp-1289"></a></var><br>
<blockquote><p>This function factorizes the symmetric square matrix <var>A</var> into the
symmetric tridiagonal decomposition Q T Q^T. On output the
diagonal and subdiagonal part of the input matrix <var>A</var> contain the
tridiagonal matrix T. The remaining lower triangular part of the
input matrix contains the Householder vectors which, together with the
Householder coefficients <var>tau</var>, encode the orthogonal matrix
Q. This storage scheme is the same as used by <span class="sc">lapack</span>. The
upper triangular part of <var>A</var> is not referenced.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_linalg_symmtd_unpack</b> (<var>const gsl_matrix * A, const gsl_vector * tau, gsl_matrix * Q, gsl_vector * diag, gsl_vector * subdiag</var>)<var><a name="index-gsl_005flinalg_005fsymmtd_005funpack-1290"></a></var><br>
<blockquote><p>This function unpacks the encoded symmetric tridiagonal decomposition
(<var>A</var>, <var>tau</var>) obtained from <code>gsl_linalg_symmtd_decomp</code> into
the orthogonal matrix <var>Q</var>, the vector of diagonal elements <var>diag</var>
and the vector of subdiagonal elements <var>subdiag</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_linalg_symmtd_unpack_T</b> (<var>const gsl_matrix * A, gsl_vector * diag, gsl_vector * subdiag</var>)<var><a name="index-gsl_005flinalg_005fsymmtd_005funpack_005fT-1291"></a></var><br>
<blockquote><p>This function unpacks the diagonal and subdiagonal of the encoded
symmetric tridiagonal decomposition (<var>A</var>, <var>tau</var>) obtained from
<code>gsl_linalg_symmtd_decomp</code> into the vectors <var>diag</var> and <var>subdiag</var>.
</p></blockquote></div>
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