## File: Linear-Algebra.html

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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 gsl_vector and 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:
Complete Orthogonal Decomposition:
Singular Value Decomposition:
Cholesky Decomposition:
Pivoted Cholesky Decomposition:
Modified Cholesky 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:
Balancing:
Linear Algebra Examples:
Linear Algebra References and Further Reading:

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