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<title>Linear Algebra - GNU Scientific Library -- Reference Manual</title>
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<h2 class="chapter">13 Linear Algebra</h2>
<p><a name="index-linear-algebra-1218"></a><a name="index-solution-of-linear-systems_002c-Ax_003db-1219"></a><a name="index-matrix-factorization-1220"></a><a name="index-factorization-of-matrices-1221"></a>
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 & Van Loan's <cite>Matrix
Computations</cite> with Level-1 and Level-2 BLAS calls for efficiency.
<p>The functions described in this chapter are declared in the header file
<samp><span class="file">gsl_linalg.h</span></samp>.
<ul class="menu">
<li><a accesskey="1" href="LU-Decomposition.html">LU Decomposition</a>
<li><a accesskey="2" href="QR-Decomposition.html">QR Decomposition</a>
<li><a accesskey="3" href="QR-Decomposition-with-Column-Pivoting.html">QR Decomposition with Column Pivoting</a>
<li><a accesskey="4" href="Singular-Value-Decomposition.html">Singular Value Decomposition</a>
<li><a accesskey="5" href="Cholesky-Decomposition.html">Cholesky Decomposition</a>
<li><a accesskey="6" href="Tridiagonal-Decomposition-of-Real-Symmetric-Matrices.html">Tridiagonal Decomposition of Real Symmetric Matrices</a>
<li><a accesskey="7" href="Tridiagonal-Decomposition-of-Hermitian-Matrices.html">Tridiagonal Decomposition of Hermitian Matrices</a>
<li><a accesskey="8" href="Hessenberg-Decomposition-of-Real-Matrices.html">Hessenberg Decomposition of Real Matrices</a>
<li><a accesskey="9" href="Hessenberg_002dTriangular-Decomposition-of-Real-Matrices.html">Hessenberg-Triangular Decomposition of Real Matrices</a>
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<li><a href="Householder-Transformations.html">Householder Transformations</a>
<li><a href="Householder-solver-for-linear-systems.html">Householder solver for linear systems</a>
<li><a href="Tridiagonal-Systems.html">Tridiagonal Systems</a>
<li><a href="Balancing.html">Balancing</a>
<li><a href="Linear-Algebra-Examples.html">Linear Algebra Examples</a>
<li><a href="Linear-Algebra-References-and-Further-Reading.html">Linear Algebra References and Further Reading</a>
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