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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`.