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A general real matrix pair (*A*, *B*) can be decomposed by
orthogonal similarity transformations into the form

A = U H V^T B = U R V^T

where *U* and *V* are orthogonal, *H* is an upper
Hessenberg matrix, and *R* is upper triangular. The
Hessenberg-Triangular reduction is the first step in the generalized
Schur decomposition for the generalized eigenvalue problem.

- Function:
*int***gsl_linalg_hesstri_decomp***(gsl_matrix **`A`, gsl_matrix *`B`, gsl_matrix *`U`, gsl_matrix *`V`, gsl_vector *`work`) This function computes the Hessenberg-Triangular decomposition of the matrix pair (

`A`,`B`). On output,*H*is stored in`A`, and*R*is stored in`B`. If`U`and`V`are provided (they may be null), the similarity transformations are stored in them. Additional workspace of length*N*is needed in`work`.