## CNF, An algorithm for numerical computation of the canonical form of a pair (A, H) consisting of an H-hermitian matrix A and a regular hermitian matrix H

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Author(s) : Ulric Kintzel

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 33-2003

MSC 2000

15A63 Quadratic and bilinear forms, inner products
15A21 Canonical forms, reductions, classification

Abstract :
Based on the work of Kagström and Ruhe for the numerical computation of the Jordan canonical form of a square complex matrix, a numerical procedure is developed here with which the canonical form of a pair (A, H) consisting of an H-hermitian matrix A and a regular hermitian matrix H can be computed. The corresponding extension of the original procedure essentially consists of a normalisation step which constitutes a generalisation of the Cholesky method.

Keywords : Indefinite scalar products, canonical form, Jordan canonical form