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14 Linear Algebra
*****************

This chapter describes functions for solving linear systems.  The
library provides linear algebra operations which operate directly on the
Note: gsl_vector. and Note: gsl_matrix. objects.  These
routines use the standard algorithms from Golub & Van Loan’s `Matrix
Computations' with Level-1 and Level-2 BLAS calls for efficiency.

The functions described in this chapter are declared in the header file
‘gsl_linalg.h’.

* LU Decomposition
* QR Decomposition
* QR Decomposition with Column Pivoting
* LQ Decomposition
* Complete Orthogonal Decomposition
* Singular Value Decomposition
* Cholesky Decomposition
* Pivoted Cholesky Decomposition
* Modified Cholesky Decomposition
* LDLT Decomposition
* Tridiagonal Decomposition of Real Symmetric Matrices
* Tridiagonal Decomposition of Hermitian Matrices
* Hessenberg Decomposition of Real Matrices
* Hessenberg-Triangular Decomposition of Real Matrices
* Bidiagonalization
* Givens Rotations
* Householder Transformations
* Householder solver for linear systems
* Tridiagonal Systems
* Triangular Systems
* Banded Systems
* Balancing
* Examples
Examples<9>.
* References and Further Reading
References and Further Reading<9>.

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