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) |

## 13.9 Hessenberg-Triangular Decomposition of Real Matrices

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`.

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