GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 13.6 Tridiagonal Decomposition of Real Symmetric Matrices

A symmetric matrix A can be factorized by similarity transformations into the form,

A = Q T Q^T

where Q is an orthogonal matrix and 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 Q T Q^T. On output the diagonal and subdiagonal part of the input matrix`A`contain the tridiagonal matrix 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 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 *`diag`, gsl_vector *`subdiag`)- 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`diag`and the vector of subdiagonal elements`subdiag`.

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

into the vectors`diag`and`subdiag`.

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |