Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773109 | Linear Algebra and its Applications | 2017 | 24 Pages |
Abstract
The set of mÃn singular matrix pencils with normal rank at most r is an algebraic set with r+1 irreducible components. These components are the closure of the orbits (under strict equivalence) of r+1 matrix pencils which are in Kronecker canonical form. In this paper, we provide a new explicit description of each of these irreducible components which is a parametrization of each component. Therefore one can explicitly construct any pencil in each of these components. The new description of each of these irreducible components consists of the sum of r rank-1 matrix pencils, namely, a column polynomial vector of degree at most 1 times a row polynomial vector of degree at most 1, where we impose one of these two vectors to have degree zero. The number of row vectors with zero degree determines each irreducible component.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Fernando De Terán, Froilán M. Dopico, J.M. Landsberg,