A canonical parametrization of the Kronecker form of a matrix pencil
The authors give an algorithm based on a theorem of \textit{A. Tannenbaum} [Invariance and system theory: Algebraic and geometric aspects; Lect. Notes Math. 845 (1981; Zbl 0456.93001)] for computing a versal deformation of the Kronecker canonical form of a matrix pencil. The deformation seen as a mapping from the manifold of parameters to the manifold of matrix pencils has to be transversal at the canonical pencil to the orbit containing the canonical pencil under the action of a pencil (composed of elements of the linear group) through conjugation. The deformation contains as few parameters as possible. The computations are carried out in the thesis of the first author [Unfolding of singular pencils with applications to control systems. PhD thesis, Drexel University (1992)]but the results are given here. They are valid only if the finite zero eigenvalues of the pencil are distinct.
scientific article; zbMATH DE number 777943
scientific article