EXTERIOR ALGEBRA AND INVARIANT SPACES OF IMPLICIT SYSTEMS - THE GRASSMANN REPRESENTATIVE APPROACH


KARCANIAS N., BASER U.

KYBERNETIKA, vol.30, no.1, pp.1-22, 1994 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 1
  • Publication Date: 1994
  • Title of Journal : KYBERNETIKA
  • Page Numbers: pp.1-22

Abstract

The matrix pencil algebraic characterisation of the families of invariant subspaces of an implicit system S(F, G) : Fz = Gz F, G is-an-element-of R(m x n), is further developed by using tools from Exterior Algebra and in particular the Grassmann Representative g(nu) of the subspace nu of the domain of (F, G). Two different approaches are considered: The first is based on the compound of the pencil C(d)(sF - G), which is a polynomial matrix and the second on the compound pencil sC(d)(F) - C(d)(G), d = dim nu. For the family of proper spaces of the domain of (F, G), m greater-than-or-equal-to d, new characterisations of the invariant spaces nu are given in terms of the properties of g(nu) as generalised eigenvectors, or invariance conditions for the spaces LAMBDA(p)nu, p = 1, 2, ..., d.