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<title>Hessenberg-Triangular Decomposition of Real Matrices - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">13.9 Hessenberg-Triangular Decomposition of Real Matrices</h3>
<p><a name="index-hessenberg-triangular-decomposition-1301"></a>
A general real matrix pair (A, B) can be decomposed by
orthogonal similarity transformations into the form
<pre class="example"> A = U H V^T
B = U R V^T
</pre>
<p>where U and V are orthogonal, H is an upper
Hessenberg matrix, and R is upper triangular. The
Hessenberg-Triangular reduction is the first step in the generalized
Schur decomposition for the generalized eigenvalue problem.
<div class="defun">
— Function: int <b>gsl_linalg_hesstri_decomp</b> (<var>gsl_matrix * A, gsl_matrix * B, gsl_matrix * U, gsl_matrix * V, gsl_vector * work</var>)<var><a name="index-gsl_005flinalg_005fhesstri_005fdecomp-1302"></a></var><br>
<blockquote><p>This function computes the Hessenberg-Triangular decomposition of the
matrix pair (<var>A</var>, <var>B</var>). On output, H is stored in <var>A</var>,
and R 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 N is needed in <var>work</var>.
</p></blockquote></div>
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