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<a name="Linear-Algebra"></a>
<div class="header">
<p>
Next: <a href="Eigensystems.html#Eigensystems" accesskey="n" rel="next">Eigensystems</a>, Previous: <a href="BLAS-Support.html#BLAS-Support" accesskey="p" rel="previous">BLAS Support</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Linear-Algebra-1"></a>
<h2 class="chapter">14 Linear Algebra</h2>
<a name="index-linear-algebra"></a>
<a name="index-solution-of-linear-systems_002c-Ax_003db"></a>
<a name="index-matrix-factorization"></a>
<a name="index-factorization-of-matrices"></a>

<p>This chapter describes functions for solving linear systems.  The
library provides linear algebra operations which operate directly on
the <code>gsl_vector</code> and <code>gsl_matrix</code> objects.  These routines
use the standard algorithms from Golub &amp; Van Loan&rsquo;s <cite>Matrix
Computations</cite> with Level-1 and Level-2 BLAS calls for efficiency.
</p>
<p>The functions described in this chapter are declared in the header file
<samp>gsl_linalg.h</samp>.
</p>

<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="LU-Decomposition.html#LU-Decomposition" accesskey="1">LU Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QR-Decomposition.html#QR-Decomposition" accesskey="2">QR Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QR-Decomposition-with-Column-Pivoting.html#QR-Decomposition-with-Column-Pivoting" accesskey="3">QR Decomposition with Column Pivoting</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complete-Orthogonal-Decomposition.html#Complete-Orthogonal-Decomposition" accesskey="4">Complete Orthogonal Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Singular-Value-Decomposition.html#Singular-Value-Decomposition" accesskey="5">Singular Value Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Cholesky-Decomposition.html#Cholesky-Decomposition" accesskey="6">Cholesky Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Pivoted-Cholesky-Decomposition.html#Pivoted-Cholesky-Decomposition" accesskey="7">Pivoted Cholesky Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Modified-Cholesky-Decomposition.html#Modified-Cholesky-Decomposition" accesskey="8">Modified Cholesky Decomposition</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Tridiagonal-Decomposition-of-Real-Symmetric-Matrices.html#Tridiagonal-Decomposition-of-Real-Symmetric-Matrices" accesskey="9">Tridiagonal Decomposition of Real Symmetric Matrices</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Tridiagonal-Decomposition-of-Hermitian-Matrices.html#Tridiagonal-Decomposition-of-Hermitian-Matrices">Tridiagonal Decomposition of Hermitian Matrices</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Hessenberg_002dTriangular-Decomposition-of-Real-Matrices.html#Hessenberg_002dTriangular-Decomposition-of-Real-Matrices">Hessenberg-Triangular Decomposition of Real Matrices</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Householder-solver-for-linear-systems.html#Householder-solver-for-linear-systems">Householder solver for linear systems</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Tridiagonal-Systems.html#Tridiagonal-Systems">Tridiagonal Systems</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Triangular-Systems.html#Triangular-Systems">Triangular Systems</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Balancing.html#Balancing">Balancing</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Linear-Algebra-Examples.html#Linear-Algebra-Examples">Linear Algebra Examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Linear-Algebra-References-and-Further-Reading.html#Linear-Algebra-References-and-Further-Reading">Linear Algebra References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

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Next: <a href="Eigensystems.html#Eigensystems" accesskey="n" rel="next">Eigensystems</a>, Previous: <a href="BLAS-Support.html#BLAS-Support" accesskey="p" rel="previous">BLAS Support</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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