A symmetric matrix @math{A} can be factorized by similarity transformations into the form,

where @math{Q} is an orthogonal matrix and @math{T} is a symmetric tridiagonal matrix.

__Function:__int**gsl_linalg_symmtd_decomp***(gsl_matrix **`A`, gsl_vector *`tau`)-
This function factorizes the symmetric square matrix
`A`into the symmetric tridiagonal decomposition @math{Q T Q^T}. On output the diagonal and subdiagonal part of the input matrix`A`contain the tridiagonal matrix @math{T}. The remaining lower triangular part of the input matrix contains the Householder vectors which, together with the Householder coefficients`tau`, encode the orthogonal matrix @math{Q}. This storage scheme is the same as used by LAPACK. The upper triangular part of`A`is not referenced.

__Function:__int**gsl_linalg_symmtd_unpack***(const gsl_matrix **`A`, const gsl_vector *`tau`, gsl_matrix *`Q`, gsl_vector *`d`, gsl_vector *`sd`)-
This function unpacks the encoded symmetric tridiagonal decomposition
(
`A`,`tau`) obtained from`gsl_linalg_symmtd_decomp`

into the orthogonal matrix`Q`, the vector of diagonal elements`d`and the vector of subdiagonal elements`sd`.

__Function:__int**gsl_linalg_symmtd_unpack_dsd***(const gsl_matrix **`A`, gsl_vector *`d`, gsl_vector *`sd`)-
This function unpacks the diagonal and subdiagonal of the encoded
symmetric tridiagonal decomposition (
`A`,`tau`) obtained from`gsl_linalg_symmtd_decomp`

into the vectors`d`and`sd`.

Go to the first, previous, next, last section, table of contents.