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Next: <a href="Bidiagonalization.html#Bidiagonalization" accesskey="n" rel="next">Bidiagonalization</a>, Previous: <a href="Hessenberg-Decomposition-of-Real-Matrices.html#Hessenberg-Decomposition-of-Real-Matrices" accesskey="p" rel="previous">Hessenberg Decomposition of Real Matrices</a>, Up: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="u" rel="up">Linear Algebra</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Hessenberg_002dTriangular-Decomposition-of-Real-Matrices-1"></a>
<h3 class="section">14.12 Hessenberg-Triangular Decomposition of Real Matrices</h3>
<a name="index-Hessenberg-triangular-decomposition"></a>

<p>A general real matrix pair (<em>A</em>, <em>B</em>) can be decomposed by
orthogonal similarity transformations into the form
</p>
<div class="example">
<pre class="example">A = U H V^T
B = U R V^T
</pre></div>

<p>where <em>U</em> and <em>V</em> are orthogonal, <em>H</em> is an upper
Hessenberg matrix, and <em>R</em> is upper triangular. The
Hessenberg-Triangular reduction is the first step in the generalized
Schur decomposition for the generalized eigenvalue problem.
</p>
<dl>
<dt><a name="index-gsl_005flinalg_005fhesstri_005fdecomp"></a>Function: <em>int</em> <strong>gsl_linalg_hesstri_decomp</strong> <em>(gsl_matrix * <var>A</var>, gsl_matrix * <var>B</var>, gsl_matrix * <var>U</var>, gsl_matrix * <var>V</var>, gsl_vector * <var>work</var>)</em></dt>
<dd><p>This function computes the Hessenberg-Triangular decomposition of the
matrix pair (<var>A</var>, <var>B</var>). On output, <em>H</em> is stored in <var>A</var>,
and <em>R</em> is stored in <var>B</var>. If <var>U</var> and <var>V</var> are provided
(they may be null), the similarity transformations are stored in them.
Additional workspace of length <em>N</em> is needed in <var>work</var>.
</p></dd></dl>




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